Question

men u=u1, n=11, x = 97.74 degree F, s = 0.82 degrees F women u= u2, n = 59,  x = 97.37 degree F s = 0.67 degrees F   

A study was done on body temperatures of men and women , The results are shown in 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. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.  

Test the claim that men have a higher mean body temperature than women.

1. What is the null and alternative hypothesis?

2. what is the test statistic?

3. What is the p value?

4. What is the conclusion of the test?

5. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

6. Does the confidence interval support the conclusion found with the hypothesis test?

Answer 1

a) null hypothesis is that the mean temperature of men and women is same

u1=u2

Alternative hypothesis is that mean temperature of man and woman is different.

u1 not equal to u2

B) test statistic to use here is two sample t test .

C) D)

In the picture

Where t test is shown and according to that at 10 degrees of freedom you can get 0.1 p value at one tailed so our p value is greater tht 0.1 which is very small.

So there is less probability of having any difference between means. And our null hypothesis will be correct.