Question

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 Fall to reject? 

a. Fail to reject the null hypothesis 

b. Reject the alternative hypothesis 

c. Reject the null hypothesis 

d. Fail to reject the alternative hypothesis

Answer 1

As we are testing here whether the male patients has more population mean than the female patients, therefore the null and the alternative hypothesis here are given as:

The standard error here is computed as:

The test statistic here is computed as:

For n₁ + n₂ - 2 = 98 degrees of freedom, the p-value here is obtained from t distribution tables as:
p = P(t₉₈ > 6.6564) = 0

As the p-value here is approx 0, the test is significant here and therefore we Reject the null hypothesis here.

C is the correct answer here.