Question

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 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 α = .05 for a one-tailed hypothesis test.

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). (1 point total: .5 for DV, .5 for IV)

b. Explain why a paired-samples t test is appropriate for answering this research question. (.5 point)

c. What would be the null and alternative hypotheses in both words and symbol notations? (1 point total: .5 for each hypothesis. Both the written form an the symbol notation need to be correct to get the .5 point for a hypothesis)

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

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

h. Calculate the t statistic for the sample of difference scores (1 point total: .5 if process is correct but answer is wrong)

Answer 1

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

(b) The paired-samples t-test is appropriate for answering this research question because every subject is tested twice.

(c) The hypothesis being tested is:

H0: µd = 0

Ha: µd > 0

(f) The standard deviation of the population of difference scores is 3.621.

(g) The standard error is 1.145.

(h) The t statistic for the sample of difference scores = 1.747

Subject	Age 65	Age 75
1	62	65
2	95	88
3	55	56
4	90	89
5	98	90
6	73	75
7	73	70
8	71	70
9	82	80
10	66	62
	76.500	mean Age 65
	74.500	mean Age 75
	2.000	mean difference (Age 65 - Age 75)
	3.621	std. dev.
	1.145	std. error
	10	n
	9	df
	1.747	t
	.0573	p-value (one-tailed, upper)