Q2) Paired-Samples t Test 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 some elderly residents, tested first when they were 70 years old and again when they were 80 years old. The researcher wants to know if there is a significant decline in memory functions from age 70 to age 80 based on this sample. In other words, it is hypothesized that the memory score at age 80 is significantly lower than the memory score at age 70. So the null and alternative hypotheses should be directional. The alpha level was set at α = .01 for a one-tailed hypothesis test. Memory score Subject Age 70 Age 80 1 72 67 2 85 79 3 69 71 4 76 69 5 82 78 6 79 78 7 88 84 8 64 64 9 65 63 10 80 82 a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared) b. Explain why a paired-samplesttest 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 difference score by subtracting each “Age 70” score from the associated “Age 80” score for each subject. Fill in the column in the table below for “difference score.” Hint: The difference score is calculated as (age 80 minus age 70), so a negative number indicates a decline in memory performance, which is the researcher’s hypothesis. Subject Difference score (Age 80 – Age 70) 1 2 3 4 5 6 7 8 9 10

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Description: Q2) Paired-Samples t Test 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 some elderly residents, tested first when they were 70 years old

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Answered: a. Identify the dependent variable…

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Q2) Paired-Samples t Test

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 some elderly residents, tested first when they were 70 years old and again when they were 80 years old. The researcher wants to know if there is a significant decline in memory functions from age 70 to age 80 based on this sample. In other words, it is hypothesized that the memory score at age 80 is significantly lower than the memory score at age 70. So the null and alternative hypotheses should be directional. The alpha level was set at α = .01 for a one-tailed hypothesis test.

	Memory score
Subject	Age 70	Age 80
1	72	67
2	85	79
3	69	71
4	76	69
5	82	78
6	79	78
7	88	84
8	64	64
9	65	63
10	80	82

a. Identify the dependent variable (this is the outcome measure) and the independent variable (this is what differentiates the two groups of data points being compared)

b. Explain why a paired-samplesttest 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 difference score by subtracting each “Age 70” score from the associated “Age 80” score for each subject. Fill in the column in the table below for “difference score.”

Hint: The difference score is calculated as (age 80 minus age 70), so a negative number indicates a decline in memory performance, which is the researcher’s hypothesis.

Subject	Difference score (Age 80 – Age 70)
1
2
3
4
5
6
7
8
9
10

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