Question

In: Statistics and Probability

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do...

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

Solutions

Expert Solution

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.


Related Solutions

Assume that the two samples are independent simple random samples selected from normally distributed populations. Do...
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 the sample of home voltages and the sample of generator voltages are from populations with the same mean. If there is a statistically significant difference, does that difference have practical significance? Day    Home (volts)   Generator (volts) 1   123.7  ...
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do...
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 0.05 significance level to test the claim that the sample of home voltages and the sample of generator voltages are from populations with the same mean. If there is a statistically significant​ difference, does that difference have practical​ significance? Day Home( volts) Generator( volts) Day Home (volts)...
Assume that two samples are independent simple random samples selected from normally distributed populations. Do not...
Assume that two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 14 cans of type B were selected and applied to similar surfaces. The​ drying​ times,​ in​ hours, were recorded. The summary statistics are below. Type​ A:   x1 = 75.7 hours​,...
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do...
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. (a) calculate the test statistic t= (b) find p-vlaue p-value= (c) Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. (Reject/no reject)...
Assume that two samples are independent simple random samples selected from normally distributed populations. Do not...
Assume that two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 14 cans of type B were selected and applied to similar surfaces. The​ drying​ times,​ in​ hours, were recorded. The summary statistics are below. Type​ A:   x overbar 1 equals...
Provided below are summary statistics for independent simple random samples from two​ normally-distributed populations. Conduct the...
Provided below are summary statistics for independent simple random samples from two​ normally-distributed populations. Conduct the required hypothesis test and obtain the specified confidence interval. xbar=12, s1=2.4, n1=20, xbar2=11, s2=7, n2=15 a) Right-tailed test, a=0.05. Find the test statistic. Find the p-value b) 90% confidence interval. Find the confidence interval
Two independent random samples were selected from two normally distributed populations with means and variances (μ1,σ21)...
Two independent random samples were selected from two normally distributed populations with means and variances (μ1,σ21) and (μ2,σ22). The sample sizes, means and variances are shown in the following table. Sample 1 n1 = 13 x̄1 = 18.2 s21 = 75.3 Sample 2 n2 = 14 x̄2 = 17.1 s2= 61.3 (a). Test H0 : σ12 = σ2against Ha : σ12 ̸= σ2. Use α = 0.05. Clearly show the 4 steps. (b). TestH0 :μ1 −μ2 =0againstHa :μ1 −μ2 >0....
The following information was obtained from two independent samples selected from two normally distributed populations with...
The following information was obtained from two independent samples selected from two normally distributed populations with unknown but equal standard deviations. n1=33;    x1¯=14.46;    s1=15.07. n2=23;    x2¯=−4.75;    s2=14.65. Find a point estimate and a 97.5% confidence interval for μ1−μ2. For the following, round all answers to no fewer than 4 decimal places. The point estimate of μ1−μ2 is: Answer The lower limit of the confidence interval is: Answer The upper limit of the confidence interval is: Answer The margin of error...
please assume all samples are simple random samples, and all populations are normally distributed. for any...
please assume all samples are simple random samples, and all populations are normally distributed. for any calculator quantity that is to be used in a further calculation involving multiplication division powers or Roots at least four significant figures should be used unless exact at McDonalds a sample of 81 drive-thru customers revealed that there drive through wait time had a mean of 4.87 minutes with standard deviation of .52 minutes a. construct a 95% confidence interval estimate (2 DP) of...
The following observations are from two independent random samples, drawn from normally distributed populations. Sample 1...
The following observations are from two independent random samples, drawn from normally distributed populations. Sample 1 [66.73, 66.8, 75.06, 58.09, 54.64, 52.83] Sample 2 [66.71, 68.17, 66.22, 66.8, 68.81] Test the null hypothesis H0:σ21=σ22 against the alternative hypothesis HA:σ21≠σ22. a) Using the larger sample variance in the numerator, calculate the F test statistic. Round your response to at least 3 decimal places.     b) The p-value falls within which one of the following ranges: p-value > 0.50 0.10 < p-value...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT