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. ( h_{0}: mu_{1} geq mu_{2} )
( h_{1}: mu_{1}<mu_{2} )
b. ( h_{0}: mu_{1} leq mu_{2} )
( h_{1}: mu_{1}>mu_{2} )
c. ( h_{0}: mu_{1}
eq mu_{2} )
( h_{1}: mu_{1}=mu_{2} )
d. ( h_{0}: mu_{1}=mu_{2} )
( h_{1}: mu_{1}
eq mu_{2} )
b. in the context of this study, what is the meaning of a type i error?
a. a type i error is committed when one rejects both the null and alternative hypotheses.
b. 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.
c. 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.
d. 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.

Explanation:

A Type I error occurs when the null hypothesis ($H_0$) is rejected when it is actually true. In this context, the null hypothesis is $H_0: \mu_1=\mu_2$ (no significant difference in mean weight - loss between the two diets). Rejecting this null hypothesis when it is true means concluding there is a significant difference when there is not.

Answer:

B. 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.