Question

Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

Males	Females
83	79
74	96
51	56
61	67
53	55
59	83
53	78
78	84
52	90
63	58
69	37
61	64
67	86
76	76
80	78
65	64
68	66
97	76
45	62
86	66
75	83
61	80
70	72
73	72
54	85
64	90
58	86
78	89
72	88
67	94
67	70
98	88
57	83
68	83
60	74
56	58
66	103
67	73
85	74
56	75

Answer 1

For Females

From the data: = 76.025, s = 13.1432

Since population standard deviation is unknown, the tcritical (2 tail) for = 0.10, for df = n -1 = 39, is 1.685

The Confidence Interval is given by ME, where

The Lower Limit = 76.025 - 3.501 = 72.524

The Upper Limit = 76.025 + 3.501 = 79.526

The 90% Confidence Interval is (72.524 , 79.526)

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For Males

From the data: = 67.325, s = 12.0669

ME = tcritical * \frac{s}{\sqrt{n}} = 1.685 * \frac{12.0669}{\sqrt{40}} = 3.215

The Lower Limit = 67.325 - 3.215 = 64.110

The Upper Limit = 67.325 + 3.215 = 70.54

The 90% Confidence Interval is (64.11 , 70.54)

_________________________________________________________

We see that there is no overlapping between the 2 confidence intervals, which means that it is safe to say that the null hypothesis H0: , will be rejected, and that there will be a statistical difference between the means.