Question

QUESTION 24 Problem 24) For a project that investigates the average weight difference by gender of patients from the Mayo clinic the researcher collected a sample of 64 male patients and another sample of 36 female patients. The researcher then calculated the sample mean of male patients as 160 lbs with a sample standard deviation of 20 lbs, and the sample mean of female patients as 140 lbs with a sample standard deviation of 10 lbs. Test the claim that the average weight of male patients is more than that of female patients. Assume unequal population standard deviation. Given the significance level equals 5. (Question) Step 4: Decision: Reject or Fail to reject? a. Fail to reject the null hypothesis ob. Reject the alternative hypothesis c. Reject the null hypothesis d. Fail to reject the alternative hypothesis

Answer 1

The provided sample means are shown below: X1 = 160 X2 = 140 Also, the provided sample standard deviations are: $1 = 20 S2 = 10 and the sample sizes are ni = 64 and n2 = 36. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mi = 42 Ha: Mi > U2

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. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the degrees of freedom are df = 96.967. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal: Hence, it is found that the critical value for this right-tailed test is te = 1.661, for a = 0.05 and df = 96.967. The rejection region for this right-tailed test is R = {t:t > 1.661}. (3) Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows:

t= X1 - 12 si s + ni n2 160 – 140 = 6.656 202 V 64 + 102 36 (4) Decision about the null hypothesis Since it is observed that t = 6.656 > t = 1.661, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0, and since p= 0) < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean ji is greater than 42, at the 0.05 significance level.

Correct option "C"

Reject the null hypothesis