Question

Suppose that the mean cholesterol level for males aged 50 is 241. An investigator wishes to examine whether cholesterol levels are significantly reduced by modifying diet only slightly. A sample of 12 patients agrees to participate in the study and follow the modified diet for 3 months. After 3 months, their cholesterol levels are measured and the summary statistics are produced on the n = 12 subjects. The mean cholesterol level in the sample is 235 with a standard deviation of 12.5. Based on the data, is there statistical evidence that the modified diet reduces cholesterol at 5% significance level? Calculate the value of the test statistic for the appropriate hypothesis

Answer 1

Solution:

Given:   the mean cholesterol level for males aged 50 is 241.

We have to test  whether cholesterol levels are significantly reduced by modifying diet only slightly.

that is: test if

Sample size = n = 12

Sample mean =

Sample Standard deviation = s = 12.5

Level of significance = 0.05

Thus hypothesis are:

Test statistic:

Find t critical value:

df = n- 1= 12 - 1 = 11

One tail area = Level of significance = 0.05

t critical value = -1.796

( it is negative, since this is left ( < ) tailed test)

Decision Rule:

Reject null hypothesis H0, if t test statistic value < t critical value =-1.796, otherwise we fail to reject H0

Since   t test statistic value = t = -1.663 > t critical value =-1.796, we fail to reject H0.

Conclusion:
At 5% significance level, there is no statistical evidence that the modified diet reduces cholesterol.