A research project has been tracking the health and cognitivefunctions of the elderly population in Arizona. The table belowshows the memory test scores from 16 elderly residents, testedfirst when they were 65 years old and again when they were 75 yearsold. The researcher wants to know if there is a significant declinein memory functions from age 65 to age 75 based on this sample. Inother words, it is hypothesized that the memory score at age 75 issignificantly lower than the memory score at age 65. So the nulland alternative hypotheses should be directional. The alpha levelwas set at α = .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 (this is what differentiates the twogroups of data points being compared). (1 point total: .5 for DV,.5 for IV)

b. Explain why a paired-samples t test is appropriatefor answering this research question. (1 point)

c. What would be the null and alternative hypotheses in bothwords and symbol notations? (2 points total: 1 for each hypothesis,.5 for written and .5 for notation)

d. Calculate the difference score by subtracting each “Age 65”score from the associated “Age 75” score for each subject. Fill inthe column in the table below for “difference score.” (1 pointtotal: deduct .5 for each error up to 1 point.)

Hint: The difference score is calculated as (age 75 minusage 65), so a negative number indicates a decline in memoryperformance, which is the researcher’s hypothesis.

Subject	Difference score (Age 75 – Age 65)
1
2
3
4
5
6
7
8
9
10

e. Calculate the mean from the sample of difference scores (1point total: .5 if process is correct but answer is wrong)

f. Estimate the standard deviation of the population ofdifference scores (1 point total: .5 if process is correct butanswer is wrong)

g. Calculate the standard error (standard deviation of thesampling distribution) (1 point total: .5 if process is correct butanswer is wrong)

h. Calculate the t statistic for the sample ofdifference scores (1 point total: .5 if process is correct butanswer is wrong)

i. Figure out the degree of freedom, and then determine thecritical t value(s) based on the type of test and thepreset alpha level. (1 point total: .5 for df, .5 for critical tvalue)

j. Compare the t statistic with the critical tvalue. Is the calculated t statistic more extreme or lessextreme than the critical t value? Then make a decisionabout the hypothesis test, stating explicitly “reject” or “fail toreject” accordingly. (2 points total: 1 for each answer)

k. Interpret the result in 1-2 sentences to answer the researchquestion (you may use the wording from the hypothesis or explain itin your own words) (1 point)

l. Calculate the standardized effect size of this hypothesistest (1 point: .5 if process is correct but answer is wrong)