# STATISTICS PROBLEMS MUST POST DATA

Scenario 1:
General Questions- Answer the following multiple choice questions (1-10). Type out your answer in the space provided, include both the letter and the selection.

1. As the length of the confidence interval for the population mean increases, the degree of confidence in the interval’s actually containing the population mean_________________?

A Stay the same

B  Increases
C  Decreases
D  Doubles

1. What value of a correlation coefficient indicates that there is a perfect positive relationship between the dependent variable, y, and the independent variable, x?

1. What value of a correlation coefficient indicates that there is no relationship between the dependent variable, y, and the independent variable, x?

1. For a fixed level of confidence when the sample size increases, the length of the confidence interval for a population mean will______________?

A     Stay the same.
B     Increase.
C     Decrease.
D     Doubles.

1. Which of the following confidence intervals will be the widest?

A     90 Percent.
B     95 Percent.
C     98 Percent.
D     80 Percent.

1. The probability of failing to detect an effect when one exists is known as a:

A     Type II error.
B     Type I error.
C     Standard error.
D     Standardized erro.r

1. Concluding that there is an effect when in reality no effect exists is known as a:

A     Type II error.
B     Type I error.
C     Standard error.
B     Type I error.

1. As the sample size increases, how is the power of the study affected?

A     It is not affected.
B     It is decreased.
C     It approaches zero.
D     It is increased.

1. When a researcher decreases the risk of making a type 1 error, the risk of making a type II error is?

A     Decreased.
B     Not Affected.
C     Increased.
D     Equal to the chance of making a type I error.

• The coefficient of determination

A     helps establish causal relationships.
B     indicates the amount of variance that two variables share.
C     is the same as the correlation coefficient.
D     is equivalent to standard deviation.

Scenario 2:

To determine the effectiveness of a new anti-hypothyroid drug, circulating thyroid stimulating hormone (TSH) levels were measured in 20 men (with hypothyroid levels) and compared to 20 men (with hypothyroid levels) that received current standard therapy as control. The data are summarized in the table below.

1. What is the null hypothesis equation for this experiment?Answer: ___________
2. Based on the statistical test that you chose, do you accept or reject the null hypothesis at P=0.05?

1. What is the 95% confidence intervals for this 2 sample t-test?

1. What is the difference of Means?

1. What is the expected standard deviation (s) within groups?
= Round to the thousandths place.

1. What is the Power of this test? Please paste your data output file in the area below.

1. Assuming that the difference of means and expected standard deviation within groups remain the same, how many samples are needed to achieve a power of 0.80? Alpha=0.05.

Scenario 3.
An insurance company is interested in determining if the severity of a burn increases the length of hospitalization for burn patients. Their data is summarized in the table below.

 Patient # Burn Severity (Percent of body burnt x the degree of burn) Burn Rank Length of Hospital Stay (hours) Hospital Stay Rank 1 1.33 1 74.1 2 2 1.25 2 74.2 1 3 1.22 3 73.5 3 4 1.11 4 72.5 4 5 1.1 5 72.1 5 6 0.99 6 58 6 7 0.95 7 56 7 8 0.88 8 48 8 9 0.8 9 38.1 9 10 0.7 10 32.2 10 11 0.56 11 28.2 11 12 0.4 12 25 12 13 0.35 13 24.5 13 14 0.32 14 24.6 14 15 0.3 15 24 15

• What statistical test would be appropriate to establish a relationship between burn severity [Burn degree (1st degree, 2nd degree, and 3rd degree) x percent of body burned] and the duration of hospitalization expressed by the number of days?

A     Pearson Product-Moment Correlation coefficient

B     Multiple Regression

C     ANOVA

D     Spearman Rank Correlation coefficient.

• What is the correlation coefficient?

• Is the correlation positive or negative?

Scenario 4:
Have you noticed the abundance of television ads for yogurt that contain probiotics? Probiotics are live micro-organisms which, when administered in adequate amounts, confer a health beneﬁt on the host. Your body needs to have a healthy amount of ”good” bacteria in the digestive tract. Many yogurts are made using active, good bacteria. A diabetes researcher hypothesized that ratio good bacteria in the digestive tract would be decreased in people that are overweight. The results are summarized in the table below.

• What type of statistical test would you use to determine if there is an association between the ratio of good bacteria and BMI?
1. Multiple linear Regression
2. ANOVA
3. Pearson Product-Moment Correlation Coefficient
4. Spearman Rank Correlation Coefficient

• Do you accept or reject the null hypothesis that there is no relationship between BMI and the ratio of good bacteria in the digestive tract at the significance level P=0.05? Please paste your data output file in the space below.

Scenario 5:

The data in the following table show the relationship of cholesterol level in men to the risk of a heart attack. The data are summarized in the table below.

• What is the slope and intercept of the regression line?

• What type of statistical test would you use to determine if there is an association between cholesterol levels and the risk of a heart attack?

A     Multiple linear Regression
B     ANOVA
C     Pearson Product-Moment Correlation Coefficient
D     Spearman Rank Correlation Coefficient

• Is the correlation positive or negative?
• What is the correlation between cholesterol levels and the risk of suffering a heart attack?

• What is the coefficient of determination for the value in the previous question? Round to the thousandths place.

Scenario 6

Suppose that you wanted to determine if a dietary supplement is effective at lowering blood pressure. You randomly select 200 people with slightly elevated blood pressure and give them either a placebo or the dietary supplement. Your research design is as follows in Table 1. You randomly select 100 people to receive the dietary supplement, and 100 people to receive the placebo. In order to determine the effectiveness of the dietary supplement, you measure systolic blood pressure. The drug was considered a success if it reduced blood pressure levels below 130 mm Hg. Your research hypothesis is: The dietary supplement will reduce blood pressure compared to placebo in people with moderately high blood pressure levels.

Table 1. Dietary Supplements and Lowering Blood Pressure

 Blood pressure below 130mmHg Blood Pressure above 130 mm Hg Placebo n=100 20 people 80 people Dietary Supplement  N=100 30 people 70 people
1. What is the null hypothesis equation for this experiment?
2. What proportion of people that received the placebo control had their blood pressure reduced at the end of the study?
3. What proportion of people that received the placebo control had their blood pressure reduced at the end of the study?
4. What statistical test would you use?
A 2 proportion z-test
B     ANOVA
C     Relative Risk
D     2 sample t-test

• Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below.Answer: ___________
• What is the 95% confidence interval for this experiment?Answer: ___________
1. What is the power of this statistical test? Please paste your data output file in the space below.

• Assuming that the expected proportions remain the same for the two groups, how many samples are needed to achieve a power level of 0.80?Answer: ___________
• Which of the following statements is correct about why you would use the Yates continuity correction when performing a Power analysis?

A     To increase your chances of making a type I error.
B     To decrease your chances of making a type I error.
C     To increase your chances of making a type II error.
D     To decrease your chances of making a type II error.

Scenario 7
A research team wanted to determine if there is an association between an artificial sweetener and developing bladder cancer. They randomly selected individuals into the exposure group (Healthy individuals that consume artificial sweetener in diet soda; 1 L/day) and compare them to a randomly selected control group (Healthy individuals that do not consume artificial sweetener; 1L/day). They followed the subjects for a period of time 10 years. The data are summarized in the table below.

Table 2. Artificial Sweetener and Bladder Cancer

 Developed Bladder Cancer Did Not Develop Bladder Cancer Consume Artificial sweetener 75 325 Do Not Consume Artificial sweetener 50 350

1. What is the null hypothesis equation for this experiment?Answer: ___________
2. What is the value of n for each group?
3. What statistical test would you use?

A     2 proportion z-test
B     ANOVA
C     Relative Risk
D     2 sample t-test

1. Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area belowAnswer: ___________

1. What is the 95% confidence interval for this experiment?
• What is the power of this statistical test? Please paste your data output file in the area below
• Assuming that the expected relative risk and expected proportion in unexposed controls remained the same, how many samples are needed to achieve a power level of 0.80? Please paste your data output file in the area below

Scenario 8:
Marijuana is the second most commonly smoked substance next to tobacco worldwide. With the recent legalization of marijuana in Colorado, a study was done to examine the relationships between chronic obstructive pulmonary disease (COPD) and smoking marijuana. Six hundred cases of males between the ages of 18 and 29 that reported to have smoked marijuana on their routinely on health physical examinations were cross matched for COPD. Six hundred age matched males were used as controls. The data are summarized in Table 3 below.
Table 3. Marijuana and Chronic Obstructive Pulmonary Disease

 Develop chronic obstructive pulmonary disease (COPD) Do not Develop chronic obstructive pulmonary disease (COPD) Total Smokes only Marijuana 81 519 600 Non smoker 58 542 600

• What is the null hypothesis equation for this experiment?
• What statistical test would you use?

A     z-test

B     ANOVA

C     Relative Risk

D     Odds ratio

• Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below.Answer: _______________

• What is the 95% confidence interval for this experiment?