Question

Study was done on body temperatures of men and women. The results are in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal.

Mean for men is 1 Mean for women is 2

n for men is 11 n for women is 59

X bar for men is 97.62 degrees F X bar for women is 97.24 degrees F

S for men is 0.88 degrees F S for women is 0.66 degrees farenheit

A. Use a 0.05 signifcance level and test the claim that men have a higher mean than women in body temp. what are the null and alternative hypotheses?

B. The test statistic is? round to two decimal places.

C. The P-value is? round to three decimal places.

D. State conclusion for the test.

E. Construct a confidence level

F. Does the confidence interval support the conclusion of the test?

Answer 1

Sample 1 Men infomation :

Mean for men =
sample size = n=11
sample mean = = 97.62
sample standard deviation for men =S= 0.88

Sample 2: Women:

Mean for men =
sample size = n=59
sample mean = = 97.24
sample standard deviation for men =S= 0.66

Claim : The men have a higher mean than women in body temp.
Claim :

Hypoyhesis :

H0: The men abd women have same body temperture .

H1:The men have a higher mean than women in body temp.

   vs   

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used

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B ) Given : the population standard deviations are equal.

Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

  

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C. The P-value is? round to three decimal places.

Test is Right tailed test , use excel command as , =TDIST(x,degrees of freedom , tails)

Where x= t test statistics =1.66 , degrees of freedom =n1+n2-2=68 , tails =1

So =TDIST(1.66,68,1) then you will get p- value as , 0.051.

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D. State conclusion for the test.

So here p- value =0.051 > 0.05 ; since fail to reject H0.

Conclusion : Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

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E. Construct a confidence level:

Here given significance level = 0.05

So confidence level = 1- significance level = 1-0.05=0.95 =95%.

at df = 68 (70) and c-level =95% , critica tc value = 1.994

Lower limit =

                     

                     

                     

Lower limit = - 0.0762

Upper limit =

               

             

             

Upper limit =0.8362

So here 95% confidence interval as ( -0.0762 , 0.8362)

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F. Does the confidence interval support the conclusion of the test?

Yes, Becuse confidence interval contains Zero .