Question

A special diet is intended to reduce the cholesterol of patients at risk of heart disease. If the diet is effective, the target is to have the average cholesterol of this group be below 200. After six months on the diet, an SRS of 150 patients at risk for heart disease had an average cholesterol level of 192 with a standard deviation of 21.

Construct a 95% confidence interval for the average cholesterol level of patients at risk for heart disease who have been on the diet for 6 months

At the 5% significance level, determine if there is sufficient evidence to claim that the diet is effective in meeting the target. Explain your answer in relation to this contex

Answer 1

H0: = 200

Ha: < 200

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 192 - 200) / ( 21 / sqrt(150) )

= -4.67

Critical value at 0.05 significance level with 149 df = -1.655

Since test statistics < -1.655, Reject the null hypothesis.

We have sufficient evidence to support the claim that the average cholesterol of this group be below 200.