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1. The confidence interval value methods for determining if the difference between two means is significant in Chapter 8 was based on the z-distribution.

A researcher is trying out a new exercise program that they expect will lower heart rate in participants and enrolls 100 individuals then randomizes them into two groups of 50. The first group is instructed to not change their habits for a month, while the second group is instructed to use the new exercise program for one month. Following the month experimental period, the research measure heart rate in both groups (reported below)

????1 = 81, standard deviation of group 1 = s1 = 20, ????2 = 73, s2 = 15

a) Report the 95% confidence interval for the difference between means using the methods of Chapter 8.

b) Is the difference in the means significant?

c) What can you conclude about the experimental hypothesis?

d) Extra credit: What are some problems with the design of the experiment above?

2. A researcher has a hypothesis that exposure to lead leads to reduced IQ. They conduct IQ tests on 25 individuals from an area that is now known to have had high levels of lead in the water.

Population mean is 100, ???? = 91, variance = s2 = 37, n = 20

a) Calculate the t statistic

b) Using alpha = 0.05, determine the critical t value, tcrit.

c) What is the 95% confidence interval for the difference in the means? (hint this may use a different tcrit)

d) Is there a difference in the means?

e) What can you conclude about the effect of exposure to lead on IQ?

3. In a study to determine the effectiveness of pain management therapy in persons with chronic pain, twenty individuals experiencing chronic pain were randomly selected. Ten of these individuals were assigned to receive pain management therapy and the other ten to receive no therapy. Descriptive statistics for each group are provided below.

No Pain Management Therapy (Sample 1)

????1 = 62, s1 = 9.7, n1 = 10

Pain Management Therapy (Sample 2)

????2 = 53, s2 = 6.4, n2 = 10

a. What type of t -test should you use?

b. What are your degrees of freedom?

c. What is the appropriate tcrit?

d. Calculate the pooled variance and standard error of the difference

e. Conduct the appropriate t-test and determine tobt.

f. What is your statistical decision?

g. What do you conclude?

4. Short answer

a. What happens to the absolute value of tcrit as df increases?

b. If a researcher reports a one-sample t-test with df = 24, how many individuals participated in this study?

c. Are sampling distributions of the mean more or less variable than the population from which they are derived?

d. When should you use a one-tailed test?

e. Describe in words Type-1 Error