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 97.75 degrees F X bar for women is 97.49 degrees F S for men is 0.83 degrees F S for women is 0.65 degrees farenheit A. Use a 0.01 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

For Men: = 97.75, s₁ = 0.83, n₁ = 11

For Women: = 97.49, s₂ = 0.65, n₂ = 59

Since we do not assume that the standard deviations are equal we use the degrees of freedom as follows.

Therefore df rounded = 13

(A) The Hypothesis:

H0:

Ha:

(B) The Test Statistic is found as below:

(C) The p value (Right Tail), df = 13 is; p value = 0.828

(D) Since p value is > , We Fail to Reject H0. There is insufficient evidence at = 0.01 to conclude that the mean temperature for men is greater than the mean temperature for women.

(E) The 99% Confidence Interval:

The tcritical (2 tail) for = 0.01, df = 13, is 3.0123

The Confidence Interval is given by ( - ) ME, where

( - ) = 97.75 – 97.49 = 0.26

The Lower Limit = 0.26 - 0.796 = -0.536

The Upper Limit = 0.26 + 0.796 = 1.056

The Confidence Interval is (-0.536 , 1.056)

Since the confidence interval contains 0 (lower limit negative and upper limit is positive), this means that the null hypothesis can be true (H0: ), and hence we fail to reject the null hypothesis. Therefore the confidence interval supports the conclusion of the test.