Question

It is generally accepted that the mean heart rate (beats per minute; bpm) of an adult human is between 65 bpm and 75 bpm, with a single average value of 72 bpm. In this case study you will test the hypothesis that the average heart rate of adults is 72 bpm (μ = 72 bpm) for all adults and then separately by gender. The distribution of heart rates is approximately normal.

1.Complete the hypothesis test for all adults(Males and Females) by performing the following steps. Use a 5% level of significance.You may assume that σ = 7.035bpm.

A.Determine if you should use a Z-Test or t-Test in conduct this hypothesis test.Explain your decision.

B.State the null and alternative hypothesis.Identify the claim.

C.Calculate the Standardized Test Statistic.

D.Calculate the p-value (or the Critical Value(s)).

E.State your decision. Explain how you made this decision.

F.State your conclusion in the context of the problem.

2.If you lowered the level of significance to 1%(in # 1), would your decision change? Explain your reasoning

Males :

70
71
74
80
73
75
82
64
69
70
68
72
78
70
75
74
69
73
77
58
73
65
74
76
72
78
71
74
67
64
78
73
67
66
64
71
72
86
72
68
70
82
84
68
71
77
78
83
66
70
82
73
78
78
81
78
80
75
79
81
71
83
63
70
75

Females:

69
62
75
66
68
57
61
84
61
77
62
71
68
69
79
76
87
78
73
89
81
73
64
65
73
69
57
79
78
80
79
81
73
74
84
83
82
85
86
77
72
79
59
64
65
82
64
70
83
89
69
73
84
76
79
81
80
74
77
66
68
77
79
78
77

Answer 1

A. Since the population standard deviation is given and sample size is large. Therefore we should use z test.

B. Hypothesis

Ho: There is no significant difference in the mean heart rate of adults and 72.

Vs

H1: The mean heart rate of adults is significantly different from 72.

C. Test statistic is

z=2.855

D. from the results of the z test in R studio,

P value is 0.004304

E. Since p value is less than 0.05(level of significance) Therefore we reject the null hypothesis at 5% level of significance.

F. We can conclude that mean adult heart rate is significantly different from 72 bpm

2. Even if we choose the significance level to 1% the p value is still smaller than the level of significance.

Therefore the decision will be the same for 1% and 5% level of significance.