Question

a powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. the powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. the liquid diet group had a mean weight loss of 44 pounds with a standard deviation of 14 pounds. conduct a hypothesis test at the 5% level. note: if you are using a student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.) part (a) state the null hypothesis.

Answer 1

The null hypothesis (H0) for the hypothesis test comparing the weight loss effects of a liquid diet to a powder diet is that the mean weight loss from the liquid diet is less than or equal to the mean weight loss from the powder diet, mathematically represented as H0: μ2 ≤ μ1.

Step-by-step explanation:

A student has asked to conduct a hypothesis test at the 5% level to determine if a liquid diet yields a higher mean weight loss than a powder diet, with a powder diet tested on 49 people and a liquid diet tested on 36 different people. When comparing two independent sample means, where population standard deviations and or variances are unknown, we employ a two-sample t-test procedure. To begin the test, we must first state our null hypothesis.

The null hypothesis (H0) for the test would typically be that the mean weight loss from the liquid diet is less than or equal to the mean weight loss from the powder diet. In a mathematical format, if μ1 represents the mean weight loss for the powder diet and μ2 represents the mean weight loss for the liquid diet, the null hypothesis can be stated as H0: μ2 ≤ μ1.