An investigator wants to test the effectiveness of a new weight loss medication at reducing BMI (kg/m²). In order for the medication to have a high chance of receiving a sizeable investment, the mean difference in BMI must be greater than or equal to 5 kg/m²in a pre/post test of BMI in participating individuals. Suppose the following table represents the results from a SRS of individuals enrolled in the study. Assume a normal approximation is acceptable.

Patient

BMI Pre-Test (kg/m²)

BMI Post-Test (kg/m²)

A

32.5

24.5

B

34.8

26.3

C

33.6

22.4

D

31.7

23.7

E

30.9

22.4

A)Is there sufficient evidence provided by the SRS to conclude that the medication is successful at reducing the overall BMI in the population by more than 5 kg/m²? (Use =0.05)

B)Construct a 95% confidence interval, and provide an interpretation.Does your interval further support your decision in the hypothesis test above?

A) Ho:₁=₂Ha:₁<₂

T statistic 21.251

Pvalue0.05

Accept the Ho, conclude that the difference in BMI is significantly different

B) CI (9.1, 13.51) no, the interval does not provides further evidence to support my decision

A) Ho: ₁=₂Ha: ₁>₂

T statistic 14.721

Pvalue 0.000

Reject the Ho, conclude that the difference in BMI is significantly different

B) CI (7.2, 10.51) yes, the interval provides further evidence to support my decision, as 0 is not within the interval.

A) Ho: ₁=₂Ha: ₁>₂

T statistic 20.123

Pvalue 0.01

Reject the Ho, conclude that the difference in BMI isnotsignificantly different

B) CI (2.1, 1.14) yes, the interval provides further evidence to support my decision, as 0 is within the interval.