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 below 200. After six months on the diet, a SRS of 50 patients at risk for heart disease had an average cholesterol of xbar= 192, with a standard deviation s=21. Is this sufficient evidence that the diet is effective in meeting the target?

A. In order to test if the diet reduces cholesterol to the desired target, state the null hypothesis and alternative hypothesis.

B. Calculate the test value to 2 decimal places.

C. Find the critical value.

D.. At a= 0.05 state your conclusion.

Answer 1

Solution :

= 200

=192

S =21

n = 50

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 200

Ha : < 200

Test statistic = t

= ( - ) / S / n

= (192-200) / 21 / 50

= −2.694

Test statistic = t = −2.694

P-value =0.0048

= 0.05  

P-value <

0.0048 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that