Question

A geriatric 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 based on this sample. The alpha level was set at α = .05 for the hypothesis test.

Memory score

Subject

Age 65

Age 75

1

62

60

2

95

62

3

55

46

4

97

89

5

98

88

6

63

80

7

73

62

8

71

75

9

86

79

10

43

41

11

51

41

12

42

50

13

51

47

14

55

85

15

52

39

16

47

56

Subject	Difference score (Age 75 – Age 65)
1	60-62 = -2
2	62-95 = -33
3	46-55 = -9
4	89-97 = -8
5	88-98 = -10
6	80-63 = 17
7	62-73 = -11
8	75-71 = 4
9	79-86 = -7
10	41-43 = -2
11	41-51 = -10
12	50-42 = 8
13	47-51 = -4
14	85-55 = 30
15	39-52 = -13
16	56-47 = 9

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

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

Answer 1

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	62	60	2
	95	62	33
	55	46	9
	97	89	8
	98	88	10
	63	80	-17
	73	62	11
	71	75	-4
	86	79	7
	43	41	2
	51	41	10
	42	50	-8
	51	47	4
	55	85	-30
	52	39	13
	47	56	-9
Average	65.063	62.5	2.563
St. Dev.	19.434	17.866	14.241
n	16	16	16

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that there is a significant decline in memory functions at the 0.05 significance level.

e)2.563

f)14.241

g) std error =Sd/ sqrt n = 14.241/ sqrt 16 = 3.56025

h) t=0.72