A research project has been tracking the health and cognitive functions of the elderly population in Arizona. The table below shows the memory test scores from 16 elderly residents, tested first when they were 65 years old and again when they were 75 years old. The researcher wants to know if there is a significant decline in memory functions from age 65 to age 75 based on this sample. In other words, it is hypothesized that the memory score at age 75 is significantly lower than the memory score at age 65. So the null and alternative hypotheses should be directional. The alpha level was set at = .05 for a one-tailed hypothesis test.

Memory score

subject: Age 65 Age 75

1 62 60

2 95 88

3 55 56

4 90 89

5 98 90

6 73 75

7 73 70

8 71 75

9 82 80

10 66 62

a. Identify the dependent variable (this is the outcome measure) and the independent variable

b. Explain why a paired-samples t test is appropriate for answering this research question.

c. What would be the null and alternative hypotheses in both words and symbol notations?

d. Calculate the mean from the sample of difference scores

e. Estimate the standard deviation of the population of difference scores

f. Calculate the standard error

g. Calculate the t statistic for the sample of difference scores

h. Figure out the degree of freedom, and then determine the critical t value(s) based on the type of test and the preset alpha level.

i. Compare the t statistic with the critical t value. Is the calculated t statistic more extreme or less extreme than the critical t value? Then make a decision about the hypothesis test, stating explicitly "reject" or "fail to reject" accordingly.

j. Calculate the standardized effect size of this hypothesis test