In a study of the effectiveness of garlic for lowering cholesterol, 17 subjects

Question

In a study of the effectiveness of garlic for lowering cholesterol, 17 subjects were treated with Garlicin, which is garlic in a processed tablet form. The measurement of interest is the change in LDL level. In the sample of 17 subjects, the sample mean was 3.205 with a sample standard deviation equal of 8.600. Assume all conditions are met to calculate a confidence interval from this data set.

(a) Find a 90% confidence interval for the average change in the LDL level. Give your answer to 3 decimal places.

(_______ , _______)

(b) Suppose that the conditions are not met. Why shouldn't we calculate a 90% confidence interval using this data set using the usual formala? (Select all that apply)

The actual confidence level might not be 90%.

As long as the sample size is over 30, then the conditions will be met so we should just repeat the study with a sample size of at least 30.

If we were to sample repeatedly and calculate a 90% confidence interval from each sample, then the percent of confidence intervals that capture the average change in the LDL level might not be 90%.

There is no problem with calculating a 90% confidence interval from the data as long as we use the T tables.

We would not capture the sample mean 90% of the time.

Explanation / Answer

Sol:

(a) Find a 90% confidence interval for the average change in the LDL level. Give your answer to 3 decimal place

sample mean=3.205

sample sd=8.6

n=17

alpha=1-0.9=0.1

alpha/2=0.1/2=0.05

n-1=17-1=16df

t crit=1.746

90% confidence interval for the average change in the LDL level.

sample mean-tcrit(samplesd/sqrt(n),sample mean-tcrit(samplesd/sqrt(n)

3.205-1.746*8.6/sqrt(17),3.205+1.746*8.6/sqrt(17)

-0.437,6.847

lower limt=-0.437

upper limit=6.847

(_______ , _______)=(-0.437,6.847)

SOlutionb:

if confidence intervals not met

confidence interval range may not be correct.

If we were to sample repeatedly and calculate a 90% confidence interval from each sample, then the percent of confidence intervals that capture the average change in the LDL level might not be 90%.

As long as the sample size is over 30, then the conditions will be met so we should just repeat the study with a sample size of at least 30

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