# MATH302 FULL COURSE

# WEEK 4

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected.

Keep in mind that your post must be made by 11:55PM EASTERN time on Wednesday during the week in which a discussion question is posed. I will evaluate your responses to each of these questions using a 0 to 10 point scale, and your contribution to each of the five Discussion Forums will count as 2 percent of the overall course grade for a total of 10 percent.

My evaluation of your post will be based on the extent to which you participated and fostered a positive and effective learning environment–for yourself and others. Participating and sharing are the keys. Naturally, simply copying someone else’s post is prohibited. Your post should reflect your understanding of the question posed. In addition to the computations you employed to arrive at your response, your post must contain comments regarding the rationale for the approach you utilized. Simply listing an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the Counting Isn’t Always Easy link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.

# WEEK 6

Suppose that the percentage annual return you obtain when you invest a dollar in gold or the stock market is dependent on the general state of the national economy as indicated below. For example, the probability that the economy will be in “boom” state is 0.15. In this case, if you invest in the stock market your return is assumed to be 25%; on the other hand if you invest in gold when the economy is in a “boom” state your return will be minus 30%. Likewise for the other possible states of the economy. Note that the sum of the probabilities has to be 1–and is.

State of economy Probability Market Return Gold Return

Boom 0.15 25% (-30%)

Moderate Growth 0.35 20% (-9%)

Week Growth 0.25 5% 35%

No Growth 0.25 (-14%) 50%

Based on the expected return, would you rather invest your money in the stock market or in gold? Why?

Keep in mind that your post must be made by 11:55PM EASTERN time on Wednesday during the week in which a discussion question is posed. I will evaluate your responses to each of these questions using a 0 to 10 point scale, and your contribution to each of the five Discussion Forums will count as 2 percent of the overall course grade for a total of 10 percent.

My evaluation of your post will be based on the extent to which you participated and fostered a positive and effective learning environment–for yourself and others. Participating and sharing are the keys. Naturally, simply copying someone else’s post is prohibited. Your post should reflect your understanding of the question posed. In addition to the computations you employed to arrive at your response, your post must contain comments regarding the rationale for the approach you utilized. Simply listing an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the Decision Alternatives link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.

# WEEK 7

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!

Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?

Keep in mind that your post must be made by 11:55PM EASTERN time on Wednesday during the week in which a discussion question is posed. I will evaluate your responses to each of these questions using a 0 to 10 point scale, and your contribution to each of the five Discussion Forums will count as 2 percent of the overall course grade for a total of 10 percent.

My evaluation of your post will be based on the extent to which you participated and fostered a positive and effective learning environment–for yourself and others. Participating and sharing are the keys. Naturally, simply copying someone else’s post is prohibited. Your post should reflect your understanding of the question posed. In addition to the computations you employed to arrive at your response, your post must contain comments regarding the rationale for the approach you utilized. Simply listing an answer is of no real value in promoting a discussion.

To make a post to this week’s Discussion Forum, click on the Using the Normal Distribution link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.

WEEK 10

Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President’s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either “approve” or “strongly approve” of the President’s handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who “approve” or “strongly approve” of the President’s handling of the crisis in the financial markets.

Now, here’s an interesting twist. If the same sample proportion was found in a sample twice as large—that is, 1150 out of 2560—how would this affect the confidence interval?

To make a post to this week’s Discussion Forum, click on the Build a Confidence Interval Estimate link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.

WEEK 12

A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds produced by the process is greater than 0.5 karat. To evaluate the profitability of the process, a sample of six diamonds was generated using this new process, with recorded weights .46, .61, .52, .48, .57, and .54 karat. Do the six measurements present sufficient evidence to indicate that the average weight of the diamonds produced by the new process is in excess of 0.5 karat? To answer this question conduct an appropriate test of hypothesis using the five step process outlined in our textbook and utilized in the solutions to the Chapter 8 review problems, which can be accessed via the link in the Assignments, Tests & Quizzes sub-section in the weekly lesson that can be found in the Lessons section of our classroom.

To make a post to this week’s Discussion Forum, click on the Testing a Hypothesis link, then click Start a New Conversation. In the title block of the dialog box that appears insert your first and last name; compose your post in the message box; and then click Post Message.

# QUIZZES

Question 1 of 20

1.0/ 1.0 Points

A variable is classified as ordinal if:

A.we track the variable through a period of time

B.the data arise from continuous measurements

C.there is a natural ordering of categories

D.there is no natural ordering of categories

Question 2 of 20

1.0/ 1.0 Points

Which of the following indicates how many observations fall into various categories?

A.The sample table

B.The tabulation scale

C.The frequency table

D.The Likert scale

Question 3 of 20

1.0/ 1.0 Points

Find the z-score for each student and indicate which one has a better relative position. An Art Major earned a grade of 46 on an exam with f$ar{x}f$ = 50 and s = 5; A Theater Major earned a grade of 70 on an exam with f$ar{x}f$ = 75 and s = 7.

A.The art major has a higher relative position than the theater major.

B.Both students have the same score.

C.The theater major has a higher relative position than the art major.

D.The higher score cannot be determined.

Question 4 of 20

1.0/ 1.0 Points

Which of the following is the graphical analog of a frequency table?

A.The scatterplot

B.The time series plot

C.The histogram

D.The contingency table

Question 5 of 20

1.0/ 1.0 Points

Which of the following are the three most common measures of central location?

A.Mean, variance, and standard deviation

B.Mean, median, and mode

C.Mean, median, and variance

D.Mean, median, and standard deviation

Question 6 of 20

1.0/ 1.0 Points

Suppose that a histogram of a data set is approximately symmetric and “bell shaped”. Approximately, what percent of the observations are within three standard deviations of the mean?

A.95%

B.99.7%

C.50%

D.68%

Question 7 of 20

0.0/ 1.0 Points

What type of sampling is being employed if the population is divided into economic classes and a sample is chosen from each economic class to be surveyed?

In A.cluster sampling

B.systematic sampling

C.stratified sampling

D.random sampling

Question 8 of 20

1.0/ 1.0 Points

The length of the box in the boxplot portrays the

A.interquartile range

B.median

C.mean

D.range

Question 9 of 20

1.0/ 1.0 Points

What kind of relationship between x and y is demonstrated by the scatter plot below?

A.A positive linear relationship

B.No linear relationship

C.This is not a scatter plot

D.A negative linear relationship

Question 10 of 20

1.0/ 1.0 Points

A population includes:

A.only households

B.all objects of interest in a particular study

C.only machines

D.only people

Question 11 of 20

1.0/ 1.0 Points

Suppose that a histogram of a data set is approximately symmetric and “bell shaped”. Approximately what percent of the observations are within one standard deviation of the mean?

A.99.7%

B.68%

C.95%

D.50%

Question 12 of 20

1.0/ 1.0 Points

The difference between the first and third quartile is called the

A.mid range

B.interquartile range

C.unimodal range

D.interdependent range

Part 2 of 3 – 2.0/ 6.0 Points

Question 13 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The histogram below represents scores achieved by 250 job applicants on a personality profile.

The histogram below represents scores achieved by 250 job applicants on a personality profile.

Sixty percent of the job applicants scored below what value? Place your answer in the blank. Do not use any stray symbols. For example, 123 would be a legitimate answer.

.30

Question 14 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.

Compute the median number of children. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 1.90

Question 15 of 20

0.0/ 1.0 Points

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.

Compute the variance of the data. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry. 2.49

Question 16 of 20

1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.

Did Well on Exam Did Poorly on Exam

Studying for Exam 60 15

Went Partying 22 53

If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitimate answer. 10.00

Question 17 of 20

1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The histogram below represents scores achieved by 250 job applicants on a personality profile.

The histogram below represents scores achieved by 250 job applicants on a personality profile.

Seventy percent of the job applicants scored above what value? Place your answer in the blank. Do not use any stray symbols. For example, 123 would be a legitimate answer.

20

Question 18 of 20

0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.

Did Well on Exam Did Poorly on Exam

Studying for Exam 60 15

Went Partying 22 53

If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying? Place your answer in the blank, rounded to 2 decimal places. Do not use a percentage sign (%). For example, 44.44 would be a legitmate answer. 20.00

Part 3 of 3 – 1.0/ 2.0 Points

Question 19 of 20

0.0/ 1.0 Points

A histogram is skewed to the left (or negatively skewed) if it has a single peak and the values of the distribution extend much further to the right of the peak than to the left of the peak.

In

True

False

Answer Key: False

Question 20 of 20

1.0/ 1.0 Points

The number of car insurance policy holders is an example of a discrete random variable

True

False

-square distribution

C.F- distribution

D.t -distribution

Question 9 of 20

1.0/ 1.0 Points

Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 26 pipes has a standard deviation of 10 inches.

A.14.0 <

has a Y-intercept of –7.5 and a slope of 2.5, then when X = 3, the actual value of Y is:

A.5

B.10

In C.0

D.unknown

Question 7 of 17

0.0/ 1.0 Points

Outliers are observations that

A.disrupt the entire linear trend

B.render the study useless

In C.lie outside the sample

D.lie outside the typical pattern of points

Question 8 of 17

1.0/ 1.0 Points

An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx.

Apartments.xlsx

At the .05 level of significance determine if the correlation between rental cost and apartment size is significant.

A.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient 0.85 exceeds 0.50.

B.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the t-test value, 7.74, is greater than the critical value 1.96.

C.No, there is not a statistically significant linear relationship between monthly rental cost and apartment size, because the sample correlation coefficient is less than .95.

D.Yes, there is a statistically significant linear relationship between monthly rental cost and apartment size, because the p-value for this test is less than .0001.

Part 3 of 8 – 0.0/ 2.0 Points

Question 9 of 17

0.0/ 2.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

Pine trees

Spruce trees

Sample size

30

35

Mean trunk diameter (cm)

45

39

Sample variance

120

140

What is the test value for this hypothesis test?

Test value: Correct2.474 Round your answer to three decimal places.

What is the critical value?

Critical value: Correct1.296 Round your answer to three decimal places.

Feedback: This is a t-test of independent samples. Use the formula for the t test value on page 480:

f[t=frac{(45-39)-0}{sqrt{frac{120}{30}+frac{140}{35}}}=2.121320f]

Using Table F (df = 29, alpha = 0.10, one-tail test) the critical t-value is 1.311.

Part 4 of 8 – 2.0/ 2.0 Points

Question 10 of 17

1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Data for a sample of 25 apartments in a particular neighborhood are provided in the worksheet Apartments in the Excel workbook Apartments.xlsx. Using the estimated regression equation found by using size as the predictor variable, find a point estimate for the average monthly rent for apartments having 1,000 square feet of space. Place your answer, rounded to the nearest whole dollar, in the blank. Correct1242 When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 123 would be a legitimate entry.

Apartments.xlsx

Question 11 of 17

1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx

Treating ILE as the response variable, use regression to fit a straight line to all 18 data points.

Using your estimated regression output, predict the indirect labor expenses for a month in which the company has 31 direct labor hours.

Place your answer, rounded to 1 decimal place, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 458.9 would be a legitimate entry. Correct525.4

Part 5 of 8 – 0.0/ 2.0 Points

Question 12 of 17

0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Are America’s top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO’s annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation 15 12 3 12 28 6 8 2

percent change for CEO 6 17 -4 12 32 -1 7 2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the test value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. Correct0.357

Question 13 of 17

0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Are America’s top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO’s annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation 15 12 3 12 28 6 8 2

percent change for CEO 6 17 -4 12 32 -1 7 2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis? Place your answer, rounded to 3 decimal places, in the blank. For example, 2.345 would be a legitimate entry. Correct1.773

Part 6 of 8 – 1.0/ 3.0 Points

Question 14 of 17

1.0/ 3.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A professor gives an exam for which there are two versions, A and B. Each student in the class is given one randomly selected version of the exam. After the exam, the professor wishes to determine if there is a difference in the level of difficulty of the two versions by determining if there is a significant difference in the mean scores. Assume ? = 0.05.

Version A

Version B

Sample size

45

65

Mean score

8.8

8.2

Sample variance

2.6

2.4

What is the test value for this hypothesis test?

What is/are the critical value(s) for this hypothesis test? If there are two critical values, give only the positive value.

What is the conclusion for this hypothesis test? Choose one.

1. There is not sufficient evidence to show that one version of the exam is more difficult than the other.

2. There is sufficient evidence to show that one version of the exam is more difficult than the other.

Part 7 of 8 – 1.0/ 1.0 Points

Question 15 of 17

1.0/ 1.0 Points

In conducting hypothesis testing for difference between two means when samples are dependent (paired samples), the variable under consideration is f$ar{D}f$ ; the sample mean difference between the pairs.

Correct

True

False

Part 8 of 8 – 2.0/ 2.0 Points

Question 16 of 17

1.0/ 1.0 Points

In a simple regression analysis, if the standard error of estimate sest = 15 and the number of observations n = 10, then the sum of the residuals squared must be 120.

True

False

Question 17 of 17

1.0/ 1.0 Points

In a simple linear regression problem, the least squares line is y’ = -3.2 + 1.3X, and the coefficient of determination is 0.7225. The coefficient of correlation must be –0.85.

True

False

# MIDTERM

Question 1 of 25 1.0/ 1.0 Points

If you classified the fruit in a basket as apple, orange, or banana, this would be an example of which level of measurement?

A.interval

B.ordinal

C.ratio

D.nominal

Part 2 of 9 – 2.0/ 2.0 Points

Question 2 of 25 1.0/ 1.0 Points

If two events are mutually exclusive, what is the probability that one or the other occurs?

A.0.25

B.Cannot be determined from the information given.

C.0.50

D.1.00

Question 3 of 25 1.0/ 1.0 Points

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A.5/8

B.2/5

C.1/8

D.1/4

Part 3 of 9 – 2.0/ 3.0 Points

Question 4 of 25 1.0/ 1.0 Points

A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled.

A.60

B.50

C.7.1

D.5.9

Question 5 of 25 1.0/ 1.0 Points

A researcher surveyed college students to study their opinion about the proposed change in smoking rules. The researcher asked a group of 30 students: 12 of them supported the change, 13 of them did not, and 5 had no opinion. This is not a binomial model because…

A….the students who strongly supported the change and those who only mildly supported the change are counted the same.

B….less than half of the students supported the change.

C.30 students are not enough for a good sample

D….there are 3 possible outcomes, not 2.

Question 6 of 25 0.0/ 1.0 Points

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that greater than 30 batteries will last at least 8 hours?

A.0.0848

B.0.9152

C.0.8594

D.0.9522

Part 4 of 9 – 5.0/ 6.0 Points

Question 7 of 25 1.0/ 1.0 Points

One reason for standardizing random variables is to measure variables with:

A.different means and standard deviations on a non-standard scale

B.similar means and standard deviations on two scales

C.dissimilar means and similar standard deviations in like terms

D.different means and standard deviations on a single scale

Question 8 of 25 1.0/ 1.0 Points

If Z is a standard normal random variable, then the value z for which P(-z < Z < z) equals 0.8764 is

A.3.08

B.1.54

C.0.3764

D.1.16

Question 9 of 25 1.0/ 1.0 Points

In a normal distribution, changing the standard deviation:

A.splits the distribution to two curves

B.shifts the curve left or right

C.makes the curve more robust

D.makes the curve more or less spread out

Question 10 of 25 1.0/ 1.0 Points

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is

A.0.1498

B.0.5328

C.0.3413

D.0.1915

Question 11 of 25 1.0/ 1.0 Points

The continuous distribution characterized by a symmetric, bell-shaped curve is the:

A.Poisson distribution

B.binomial distribution

C.normal distribution

D.exponential distribution

Question 12 of 25 0.0/ 1.0 Points

The standard deviation of a probability distribution is a:

A.measure of skewness of the distribution

B.measure of variability of the distribution

C.measure of relative likelihood

D.measure of central location

Part 5 of 9 – 1.0/ 1.0 Points

Question 13 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.

77 81 74 77 79 73 80 85 86 73

83 84 81 73 75 91 76 77 95 76

90 85 92 84 81 64 75 90 78 78

82 78 86 86 82 70 76 78 72 93

What is the mean score on this exam? Place your answer, rounded to two decimal places in the blank. For example, 65.78 would be a legitimate entry. 80.40

Part 6 of 9 – 1.0/ 2.0 Points

Question 14 of 25 0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.

x 0 1 2 3 4 5 6

P (X=x) 0.55 0.15 0.10 0.10 0.04 0.03 0.03

Find P(1 < X < 5). Place your answer, rounded to two decimal places in the blank. For example, 0.56 would be a legitimate entry. 1.14

Question 15 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

Number of Products Purchased

Brands Purchased Fewer Same More Total

Same 10 14 24 48

Changed 262 82 8 352

Total 272 96 32 400

What is the probability that a consumer selected at random purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank. 0.6800

Part 7 of 9 – 2.0/ 2.0 Points

Question 16 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that only one of the questionnaires will be returned? Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry. 0.42

Question 17 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

If you have six books, but there is room for only four books on the shelf, in how many ways can these books be arranged on the shelf? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry. 360

Part 8 of 9 – 4.0/ 6.0 Points

Question 18 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry. 73

Question 19 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

Find the probability that the mean of the sample is greater than $460. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate answer. 0.0228

Question 20 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry. .1587

Question 21 of 25 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

In a particular region of Cape Cod, it is known that lobstermen trap on average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

Place your answer, rounded to four decimal places, in the blank. 0.2468 When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 0.1234 would be a legitimate entry.

Question 22 of 25 0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry. 140

Question 23 of 25 0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

Find the mean of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 123 would be a legitimate entry. 5

Part 9 of 9 – 1.0/ 2.0 Points

Question 24 of 25 0.0/ 1.0 Points

A random variable X is normally distributed with a mean of 100 and a variance of 25. Given that X = 110, its corresponding Z- score is 0.40.

True

False

Question 25 of 25 1.0/ 1.0 Points

If Z is a standard normal variable, then P(Z = 1) = 0.3413.

True

False

# FINAL

Question 1 of 23 1.0/ 1.0 Points

A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.

Machine

Shift A B C D

1 41 20 12 16

2 31 11 9 14

3 15 17 16 10

A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.

B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.

C.The number of breakdowns is dependent on the shift, because the p-value is .07.

D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.

Question 2 of 23 1.0/ 1.0 Points

The data presented in the table below resulted from an experiment in which seeds of 5 different types were planted and the number of seeds that germinated within 5 weeks after planting was recorded for each seed type. At the .01 level of significance, is the proportion of seeds that germinate dependent on the seed type?

Seed Type Observed Frequencies

Germinated Failed to Germinate

1 31 7

2 57 33

3 87 60

4 52 44

5 10 19

A.Yes, because the test value 16.86 is greater than the critical value of 13.28

B.Yes, because the test value 16.86 is less than the critical value of 14.86

C.No, because the test value 16.86 is greater than the critical value of 13.28

D.No, because the test value 13.28 is less than the critical value of 16.86

Part 2 of 16 – 3.0/ 3.0 Points

Question 3 of 23 1.0/ 1.0 Points

In a simple linear regression analysis, the following sum of squares are produced:

= 500

= 100

= 400

The proportion of the variation in Y that is explained by the variation in X is:

A.25%

B.80%

C.50%

D.20%

Question 4 of 23 1.0/ 1.0 Points

In regression analysis, the variable we are trying to explain or predict is called the

A.dependent variable

B.independent variable

C.regression variable

D.residual variable

Question 5 of 23 1.0/ 1.0 Points

In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:

A.smallest sum of squared residuals

B.largest number of points on the line

C.smallest number of outliers

D.largest sum of squared residuals

Part 3 of 16 – 2.0/ 2.0 Points

Question 6 of 23 1.0/ 1.0 Points

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7

Before 158 189 202 353 416 426 441

After 284 214 101 227 290 176 290

Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?

A.t = 2.7234

B.p = 2.7234

C.z = 1.8424

D.t = 1.8424

Question 7 of 23 1.0/ 1.0 Points

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient 1 2 3 4 5 6 7

Before 158 189 202 353 416 426 441

After 284 214 101 227 290 176 290

Suppose you wanted to conduct a test of hypothesis to determine if there is sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the p-value associated with the test of hypothesis you would conduct?

A.p = .942597

B.p = .057493

C.p = .114986

D.p = .885014

Part 4 of 16 – 2.0/ 3.0 Points

Question 8 of 23 0.0/ 1.0 Points

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

At the ? = .01 level of significance, what is your conclusion?

A.Do not reject H0. At the = .01 level of significance there is not sufficient evidence to suggest that this technician’s true variance is greater than the target accuracy.

B.Reject H0. At the = .01 level of significance, there is enough evidence to support the claim that this technician’s variance is larger than the target accuracy.

C.Cannot determine

D. Reject H0. At the = .01 level of significance, there is not enough evidence to support the claim that this technician’s true variance is larger than the target accuracy.

Question 9 of 23 1.0/ 1.0 Points

A null hypothesis can only be rejected at the 5% significance level if and only if:

A.a 95% confidence interval includes the hypothesized value of the parameter

B.a 95% confidence interval does not include the hypothesized value of the parameter

C.the null hypotheses includes sampling error

D.the null hypothesis is biased

Question 10 of 23 1.0/ 1.0 Points

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

At the ? = .05 level of significance, does the nutritionist have enough evidence to reject the writer’s claim?

A.Yes

B.No

C.Cannot Determine

Part 5 of 16 – 2.0/ 2.0 Points

Question 11 of 23 1.0/ 1.0 Points

The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.

A.n + 1

B.n – 1

C.n

D.n – 2

Question 12 of 23 1.0/ 1.0 Points

In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that SAT test scores are normally distributed with a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?

A.1330

B.1400

C.1250

D.1100

Part 6 of 16 – 1.0/ 1.0 Points

Question 13 of 23 1.0/ 1.0 Points

If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

A.equal to the mean

B.to the left of the mean

C.to the right of the mean

D.one standard deviation higher than the mean

Part 7 of 16 – 1.0/ 1.0 Points

Question 14 of 23 1.0/ 1.0 Points

In a small town, 60% of the households have dogs. If 5 households are randomly selected, what is the probability that at least 4 of them have dogs?

A.0.337

B.3

C.0.8

D.0.259

Part 8 of 16 – 1.0/ 1.0 Points

Question 15 of 23 1.0/ 1.0 Points

If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to

A.0.0

B.1.0

C.0.5

D.any value between 0.5 and 1.0

Part 9 of 16 – 3.0/ 3.0 Points

Question 16 of 23 3.0/ 3.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

A sport preference poll yielded the following data for men and women. Use a 5% significance level and test to determine if sport preference and gender are independent.

Sport Preferences of Men and Women

Basketball Football Soccer

Men 20 25 30 75

Women 18 12 15 45

38 37 45 120

What is the test value for this hypothesis test?

What is the critical value for this hypothesis test?

What is the conclusion for this hypothesis test? Choose one.

1. There is sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender.

2. There is not sufficient evidence to support the claim that one’s sport preference is dependent on one’s gender.

Part 10 of 16 – 1.0/ 1.0 Points

Question 17 of 23 1.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Store Shelf Space(X) Weekly Sales(Y)

1 10 2.0

2 10 2.6

3 10 1.8

4 15 2.3

5 15 2.8

6 15 3.0

7 20 2.7

8 20 3.1

9 20 3.2

10 25 3.0

11 25 3.3

12 25 3.5

Using the equation of the regression line for these data, predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.

Place your answer, rounded to 3 decimal places , in the blank. Do not use a dollar sign. For example, 2.345 would be a legitimate entry. 2.442

Part 11 of 16 – 0.0/ 1.0 Points

Question 18 of 23 0.0/ 1.0 Points

For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies.

If you are interested in determining if there is sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies, what is the p-value associated with such a test of hypothesis?

Place your answer, rounded to 4 decimal places, in the blank. For example, .0123 would be a legitimate entry. 1.18