MATH221 Week 5 Homework (July 2019)

MATH 221 Statistics for Decision Making

Week 5 Homework

Question 1 From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5DA. Concept and meaning of confidence intervals (Links to an external site.) (DOCX)

(21.78, 22.60)

(19.24, 24.14)

(20.71, 22.67)

(20.86, 22.52)

Question 2 If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

Homework Help:

5DB. Finding margin of error from given confidence interval (Links to an external site.) (DOCX)

43.83

18.14

4.54

9.07

Question 3 If a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics would be better?

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

narrow confidence interval at low confidence level

wide confidence interval with high confidence level

wide confidence interval with low confidence level

narrow confidence interval at high confidence level

Question 4 Which of the following are most likely to lead to a narrow confidence interval?

Homework Help:

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

large standard deviation

large mean

small sample size

small standard deviation

Question 5 If you were designing a study that would benefit from very disperse data points, you would want the input variable to have:

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

a small margin of error

a large standard deviation

a large sample size

a large mean

Question 6 The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 56.96. What should be done about the production line?

Homework Help:

5DE. Given a confidence interval and sample mean, what decisions can be made (Links to an external site.)(DOCX)

Keep the line operating as it is close to the confidence interval

Stop the line as it is close to the confidence interval

Keep the line operating as it is outside the confidence interval

Stop the line as it is outside the confidence interval

Question 7 In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 31.9 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

(31.90, 32.44)

(31.27, 32.53)

(31.36, 31.90)

(31.36, 32.44)

Question 8 What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

(83.1, 88.1)

(84.6, 86.6)

(84.4, 86.8)

(84.7, 86.5)

Question 9 If two samples A and B had the same mean and standard deviation, but sample A had a smaller sample size, which sample would have the wider 95% confidence interval?

Homework Help:

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

Sample B as it has the larger sample

Sample B as its sample is more disperse

Sample A as it has the smaller sample

Sample A as it comes first

Question 10 Why might a company use a lower confidence interval, such as 80%, rather than a high confidence interval, such as 99%?

Homework Help:

5DF. Why companies in different industries use different levels of confidence (Links to an external site.) (DOCX)

They are in the medical field, so cannot be so precise

They make children’s toys where imprecision is expected

They make computer parts where they are too small for higher accuracy

They track the migration of fish where accuracy is not as important

Question 11 Determine the minimum sample size required when you want to be 95% confident that the sample mean is within two units of the population mean. Assume a population standard deviation of 4.3 in a normally distributed population.

Homework Help:

5VB. Calculating minimum sample size (Links to an external site.) (1:52)

5DG. Why set a minimum sample size (DOCX)

18

16

22

20

Question 12 Determine the minimum sample size required when you want to be 99% confident that the sample mean is within 0.50 units of the population mean. Assume a population standard deviation of 1.4 in a normally distributed population.

Homework Help:

5VB. Calculating minimum sample size (Links to an external site.) (1:52)

5DG. Why set a minimum sample size (DOCX)

52

30

31

53

Question 13 In a sample of 10 CEOs, they spent an average of 12.5 hours each week looking into new product opportunities with a sample standard deviation of 4.9 hours. Find the 95% confidence interval. Assume the times are normally distributed.

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5VC. Using z or t (Links to an external site.) (2:13)

(9.5, 15.5)

(9.4, 16.4)

(7.6, 17.4)

(9.0, 16.0)

Question 14 In a sample of 18 kids, their mean time on the internet on the phone was 28.6 hours with a sample standard deviation of 5.6 hours. Which distribution would be most appropriate to use, when we assume these times are normally distributed?

Homework Help:

5VC. Using z or t (Links to an external site.) (2:13)

z distribution as the population standard deviation is known while the times are assumed to be normally distributed

t distribution as the population standard deviation is unknown while the times are assumed to be normally distributed

t distribution as the sample standard deviation is unknown

z distribution as the sample standard deviation always represents the population

Question 15 Under a time crunch, you only have time to take a sample of 10 water bottles and measure their contents. The sample had a mean of 20.05 ounces with a sample standard deviation of 0.3 ounces. What would be the 90% confidence interval, when we assumed these measurements are normally distributed?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5VC. Using z or t (Links to an external site.) (2:13)

(19.92, 20.18)

(19.89, 20.21)

(19.88, 20.22)

(19.75, 20.35)

Question 16 Say that a supplier claims they are 99% confident that their products will be in the interval of 50.02 to 50.38. You take samples and find that the 99% confidence interval of what they are sending is 50.03 to 50.37. What conclusion can be made?

Homework Help:

5VD. Comparing sample confidence intervals with given intervals (Links to an external site.) (3:43)

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

The supplier products have a lower mean than claimed

The supplier products have a higher mean than claimed

The supplier is less accurate than they claimed

The supplier is more accurate than they claimed

Question 17 Market research indicates that a new product has the potential to make the company an additional $1.6 million, with a standard deviation of $2.0 million. If these estimates were based on a sample of 8 customers from a normally distributed data set, what would be the 95% confidence interval?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5VC. Using z or t (Links to an external site.) (2:13)

(-0.40, 3.60)

(0.00, 3.27)

(-0.07, 3.27)

(0.21, 3.00)

Question 18 In a sample of 20 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 162.5 degrees with a sample standard deviation of 14.1 degrees. What would be the 95% confidence interval for the temperature of your cup of coffee?

Homework Help:

5VA. Calculating confidence intervals (Links to an external site.) (4:04)

5VC. Using z or t (Links to an external site.) (2:13)

(156.32, 168.68)

(155.90, 169.10)

(148.40, 176.60)

(157.96, 167.04)

Question 19 In a situation where the sample size was 46 while the population standard deviation was decreased, what would be the impact on the confidence interval?

Homework Help:

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

It would become narrower due to less dispersion in values

It would remain the same as standard deviation does not impact confidence intervals

It would become wider due to more dispersion in values

It would become narrower with fewer values

Question 20 You needed a supplier that could provide parts as close to 76.8 inches in length as possible. You receive four contracts, each with a promised level of accuracy in the parts supplied. Which of these four would you be most likely to accept?

Homework Help:

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

5DF. Why companies in different industries use different levels of confidence (Links to an external site.) (DOCX)

Mean of 76.8 with a 99% confidence interval of 76.6 to 77.0

Mean of 76.8 with a 95% confidence interval of 76.6 to 77.0

Mean of 76.8 with a 90% confidence interval of 76.6 to 77.0

Mean of 76.800 with a 99% confidence interval of 76.5 to 77.1