Question

A recent study compared different psychological therapies for teenage girls suffering form anorexia, an eating disorder that cause them to become dangerously underweight. Each girl’s weight was measured before and after a period of therapy. The variable of interest was the weight change, defined as (weight at the end - weight at the beginning). Using hypothesis H₀ : µ = 0 and H_a : µ 6= 0 about the population mean weight change µ, we get a P-value of 0.02.

a) What would the decision be for a significant level of 0.05? Interpret in context.

b) If the decision in part a) is in error, what type of error is it?

c) Suppose the significance level were instead 0.01. What decision would you make, and if it is in error, what type of error is it?

Answer 1

Null Hypothesis H0:

Alternative Hypothesis Ha:

P Value= 0.02

a) For alpha= 0.05

Decision: Since P value is is smaller than 0.05 level of significance therefore we reject null hypothesis and conclude that the there is change in weight.

b) If the decison in Part (a) is wrong then it is Type I error . Rejecting Null hypothesis when it is True.

c) For alpha= 0.01

P value= 0.02

Decison: Decision: Since P value is is greater than 0.01 level of significance therefore we Do Not Reject the null hypothesis H0.

If Decision is error then it is called Tpe II error. Retaining Null hypothesis when it is false.