# School of Public Health

Hypothesis testing and t-tests

1. A researcher randomly assigns subjects with hypertension to one of three drug doses, then measures the heart rate of each group after administering the drug. The purpose of the study is to see what effect the drug has on heart rates. What are the independent variable(s) and dependent variable(s) in this study? (1 point)

independent variable:

dependent variable:

2.Research report: "Because we had no idea whether the treatment would increase or decrease mean blood pressure compared to the pretest value, we decided to do a one-tailed t-test". Is this logic valid? If not, why? Briefly explain. (2 points)

3.What is the basic underlying meaning of p = 0.01 from a statistical test? (1 point)

a. Data so far from H0 would have occurred 1 time in 100 if H0 were true.

b. Data so far from H0 would have occurred 1 time in 100 if HA were true.

c. H0 has a 1 in 100 probability of being true.

d. HA has a 1 in 100 probability of being true.

4.Research report: "The treated and untreated groups had means of 40 and 45 respectively. The t-test to compare the groups returned p = 0.02." Using 0.05 as alpha, these results mean (1 point)

a.98% of the subjects in the treated group did better than the control mean.

b.The treatment is probably not effective for this dependent variable.

c.The treatment has produced a sample mean difference unlikely to arise by chance.

d.The difference is statistically significant.

e.c and d.

5.If alpha is set to 0.02, which of the following p values is/are significant? Circle all that apply (1 point). 0.001 0.01 0.03 0.05 0.50 0.99

6. Which of the following would be acceptable null hypotheses? (1 point)

a. The mean of population 1 is greater than the mean of population 2.

b. The mean of population 1 is less than the mean of population 2.

c. The mean of population 1 is NOT equal to the mean of population 2.

d. The mean of population 1 is EQUAL to the mean of population 2.

e. a, b, or c

7.A researcher obtains t = 2.8. This is a one-tailed t-test. What p-value would best be reported? There were two groups, each with 6 subjects. (1 point)

a. p < 0.05

b. p < 0.025

c. p < 0.02

d. p < 0.01

e. p < 0.005

8.A sample of 16 healthy patients has a mean blood albumin level of 4.25, and standard deviation of 0.4. A sample of 16 patients with early acute leukemia is found to have a mean of 3.8, standard deviation of 0.5. What t value would you obtain for an unpaired t-test comparing the two sample means? (2 points - 1 for t, 1 for p)

What p value do you get, two-tailed?

9.A researcher has a power of 80% and alpha = 0.05. If there in truth is a difference like the one used in the power analysis between the conditions being compared, how likely is the researcher to commit a type II error? (Specific percentage, please. 1 point).

10.A researcher wants to compare 50 smokers and 50 nonsmokers on mean heart rate. Heart rate is normally distributed in these data, and the standard deviations in the two groups are similar. The two groups are completely independent samples. Would you use a t-test? If so, which type? Explain your answer. (2 points)

11.Subjects receive drug A for a week, after which their blood hemoglobin is measured. Subjects then receive drug B for a week, after which their blood hemoglobin is again measured. Changes in hemoglobin are normally distributed. Could you use a t-test to see if there was a change? If so, which type? Explain your answer. (2 points)

12.To compare the percentage of men who answer yes to the percentage of women who answered yes to a certain questionnaire item, would you use a t-test? If so, which type? Explain your answer. (2 points)

13.The following data are obtained in a group of agoraphobia patients before and after a 2-day intensive conditioning program. Agoraphobia (fear of open spaces, unfamiliar places, etc...) is very resistant to change, and does not normally improve on its own. Data is a 5-point scale from 1 = no avoidance (thus normal willingness to participate in activities) to 5 = complete avoidance. A number of situations are included, so the resulting score is an average for the subject and need not be 1, 2, 3, 4, or 5 exactly. (Data based on published studies, but there was no raw data available, so specific values are invented)

Before After

5.0 3.0

4.5 3.2

4.3 4.3

4.0 3.1

3.8 3.5

3.5 3.5

3.4 2.0

3.0 1.5

2.5 1.1

Perform a paired t-test on these data, one-tailed. Interpret the results.

#### Solution Summary

This solution addresses 13 questions addressing various hypothesis testing techniques.