Question

a study compared weight loss between patients on diet a and patients on diet b. patients on diet a lost a mean of 7.6 pounds in six months, whereas patients on diet b lost a mean of 7.3 pounds in six months. suppose that the study was based on a sample of 400 patients on diet a and 400 patients on diet b, and the standard deviation of the amount lost was 3.6 pounds for diet a and 2.9 pounds for diet b. complete parts (a) through (d)

a type i error is committed when one concludes that there is a significant difference in mean weight loss between the two diets when there is not a significant difference.
a type i error is committed when one concludes that there is not a significant difference in mean weight loss between the two diets when there is a significant difference
a type i error is committed when the null hypothesis is rejected when there is a significant difference in the mean weight loss between the two diets.
c. in the context of this study, what is the meaning of a type ii error?
a. a type ii error is committed when one concludes that there is a significant difference in mean weight loss between the two diets when there is not a significant difference.
b. a type ii error is committed when one does not reject both the null and the alternative hypothesis.
c. a type ii error is committed when one concludes that there is not a significant difference in mean weight loss between the two diets when there is indeed a significant difference.
d. a type ii error is committed when one concludes that there is not a significant difference in mean weight loss of only diet a.

Explanation:

A Type II error occurs when we fail to reject a false null hypothesis. In hypothesis testing for the difference in means between two diets (Diet A and Diet B), the null hypothesis \(H_0:\mu_A-\mu_B = 0\) (no significant difference in mean weight - loss) and the alternative hypothesis \(H_1:\mu_A-\mu_B
eq0\) (significant difference in mean weight - loss). A Type II error means we conclude there is no significant difference (fail to reject \(H_0\)) when in reality there is a significant difference ( \(H_0\) is false).

Answer:

C. A Type II error is committed when one concludes that there is not a significant difference in mean weight loss between the two diets when there is indeed a significant difference.