Question

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure.

Women   Men
71.0   70.0
94.0   64.0
79.0   67.0
65.0   60.0
73.0   63.0
79.0   71.0
58.0   58.0
51.0   40.0
71.0   67.0
87.0   66.0
67.0   82.0
60.0   74.0
73.0   55.0
61.0   75.0
67.0   52.0
89.0   91.0
57.0   77.0
83.0   81.0
69.0   61.0
62.0   73.0
71.0   80.0
71.0   102.0
89.0   61.0
69.0   79.0
67.0   73.0
67.0   83.0
71.0   65.0
82.0   67.0
75.0   56.0
91.0   85.0
61.0   78.0
69.0   56.0
76.0   63.0
90.0   65.0
86.0   71.0
60.0   48.0
78.0   65.0
83.0   77.0
78.0   74.0
83.0   53.0
77.0   69.0
59.0   63.0
64.0   69.0
76.0   78.0
61.0   71.0
69.0   75.0
65.0   66.0
55.0   89.0
67.0   67.0
71.0   75.0
64.0   48.0
71.0   87.0
77.0   89.0
66.0   68.0
83.0   72.0
60.0   66.0
94.0   75.0
57.0   89.0
75.0   55.0
75.0   91.0
58.0   83.0
77.0   88.0
65.0   94.0
93.0   88.0
46.0   87.0
46.0   102.0
65.0   71.0
70.0   81.0
57.0   69.0
70.0   63.0
65.0   65.0
71.0   69.0
70.0   69.0
65.0   53.0
75.0   76.0
64.0   63.0
71.0   80.0
57.0   91.0
58.0   79.0
79.0   88.0
72.0   65.0
71.0   71.0
64.0   79.0
67.0   75.0
85.0   57.0
55.0   65.0
76.0   84.0
73.0   73.0
51.0   68.0
89.0   68.0
58.0   69.0
81.0   73.0
81.0   73.0
76.0   68.0
65.0   78.0
71.0   68.0
62.0   51.0
87.0   65.0
56.0   73.0
75.0   66.0
76.0   77.0
90.0   53.0
65.0   53.0
69.0   66.0
80.0   85.0
42.0   85.0
73.0   72.0
71.0   80.0
46.0   69.0
71.0   56.0
88.0   85.0
77.0   83.0
69.0   58.0
68.0   68.0
71.0   63.0
79.0   66.0
65.0   72.0
97.0   64.0
67.0   65.0
72.0   79.0
62.0   86.0
67.0   76.0
69.0   95.0
74.0   96.0
59.0   75.0
69.0   79.0
55.0   75.0
55.0   55.0
71.0   77.0
68.0   73.0
74.0   51.0
77.0   75.0
40.0   81.0
72.0   67.0
57.0   82.0
68.0   73.0
80.0   82.0
65.0   53.0
73.0   83.0
64.0   98.0
66.0   68.0
56.0   68.0
95.0   68.0
71.0   71.0
63.0   46.0
84.0   57.0
54.0   50.0
67.0
44.0
81.0
61.0
74.0
   70.0

Answer 1

I used R software to solve this question.

R codes and output:

> d=read.table('data.csv',header=T,sep=',')

> head(d)

Women Men

1    71 70

2    94 64

3    79 67

4    65 60

5    73 63

6    79 71

> attach(d)

The following objects are masked from d (pos = 3):

    Men, Women

> t.test(Women,Men)

            Welch Two Sample t-test

data: Women and Men

t = -1.213, df = 295.62, p-value = 0.2261

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-4.246489 1.007869

sample estimates:

mean of x mean of y

69.91447 71.53378

Hypothesis:

Test statistic, t = -1.213

Degrees of freedom =  295.62,

p-value = 0.2261

Since p-value is greater than 0.01, we accept null hypothesis and conclude that women and men have the same mean diastolic blood pressure.