Question

Refer to the accompanying data set and construct a 95​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

Construct a 95​% confidence interval of the mean pulse rate for adult females.

Males
86
71
52
60
54
64
53
76
51
59
73
60
63
76
80
63
65
97
40
89
74
63
73
70
52
65
57
81
72
66
63
97
56
64
57
59
68
69
86
60

Females
79
96
55
69
53
82
76
85
89
56
38
64
86
79
78
64
66
77
62
66
81
84
72
76
88
89
90
87
91
94
71
90
82
81
74
55
97
72
74
74

Answer 1

Solution:

95​% confidence interval estimate of the mean pulse rate of adult females

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 76.05

S = 13.23544193

n = 40

Confidence level = 95%

df = n – 1 = 39

Critical t value by using t-table = 2.0227

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 76.05 ± 2.0227*13.23544193/sqrt(40)

Confidence interval = 76.05 ± 4.2329

Lower limit = 76.05 - 4.2329 = 71.82

Upper limit = 76.05 + 4.2329 = 80.28

Confidence interval = (71.82, 80.28)

95​% confidence interval estimate of the mean pulse rate of adult males

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 67.1

S = 12.60402866

n = 40

Confidence level = 95%

df = n – 1 = 39

Critical t value by using t-table = 2.0227

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 67.1 ± 2.0227*12.60402866/sqrt(40)

Confidence interval = 67.1 ± 4.0310

Lower limit = 67.1 - 4.0310 = 63.07

Upper limit = 67.1 + 4.0310 = 71.13

Confidence interval = (63.07, 71.13)

From above two intervals, it is observed that the width of the interval for adult females is more than the width of the interval for the adult males.