Part 1: Consider the following situation: When 40 people use the Weight Watchers diet for one year, their mean weight loss was = 3.0 pounds. The historical standard deviation is σ = 4.9 pounds (based on data from "Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction," by Dansinger, et al., Journal of the American Medical Association, Vol. 293, No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0.

What are the null and alternate hypotheses?

What would be the result of a Type 1 error in this situation?

What would be the result of a Type 2 error? Express your answers in the context of the situation given.

 

0.01 significance level to test the claim that the mean weight loss is greater than 0

What are the null and alternate hypotheses?

H0; μ > 0

H1; ≤0;

z = 3.872

We check for z value from the z tables at 0.01 significant level.

z= 2.58.

we compare the z value. since z value (3.872) is greater than absolute z value(2.58). we fail to reject null hypothesis. the mean weight loss is greater than 0.

What would be the result of a Type 1 error in this situation?

Type I is when we reject null hypothesis when it is true. In this case we have accepted the null hypothesis thus no Type 1 error.

What would be the result of a Type 2 error? Express your answers in the context of the situation given.

Type II error is the error that occurs when the null hypothesis is accepted when it is not true.

In this analysis we find that the mean weight loss is greater than 0, thus accepting Null hypothesis when it is true. No Type II error.

Step-by-step explanation

0.01 significance level to test the claim that the mean weight loss is greater than 0

Hypothesis.

H0; μ > 0

H1; ≤0;

n=40;

s=4.9

μ =0

 x? = 3.0

z = ?n?s?x?−μ?? = ?40?4.9?3−0?? = 3.872

z = 3.872

We check for z value from the z tables at 0.01 significant level.

z= 2.58.

we compare the z value.