Question

6) A researcher studied how two diets compare in terms of weight loss after 6 months. 40 people used the first diet. Their sample mean was 44, and their sample standard deviation was 10. 60 people used the first diet. Their sample mean was 37, and their sample standard deviation was 15. Give the 92% confidence interval for the true difference between the mean weight losses.

7)

Refer to the information in the previous question.   

         Can we conclude that the two diets really differ in terms of the mean weight loss?

(Answer in format yes or no, because the p-value < ___ .)

Answer 1

We would be looking at the first question here that is Q6.

Q6) The standard error here is computed as:

For n₁ + n₂ - 2 = 98 degrees of freedom, we have from t distribution tables here:
P( t₉₈ < 1.769) = 0.96

Therefore P( -1.769 < t₉₈ < 1.769) = 0.92

Therefore the 92% confidence interval here is obtained as:

This is the required 95% confidence interval here.