Question

7. A nutritionist wants to determine whether people who regularly drink one protein shake per day have different cholesterol levels than people in general. In the general population, cholesterol is normally distributed with μ = 190 and σ = 30. A person followed the protein shake regimen for two months and his cholesterol is 155. Use the 1% significance level to test the nutritionist’s idea.

1. Use the five steps of hypothesis testing. Explicitly label each of these five steps.
2. Draw a curve and label the cutoff(s), rejection region(s), and sample’s score.
3. Provide an interpretation of the finding.

Interpretation: One sentence conclusion of the hypothesis test that should be free of statistical jargon

8. A forensic psychologist studying a new type of polygraph (lie detector) test. On average, the older polygraph test is 75% accurate, with a standard deviation of 6.5%. With the new polygraph test, the operator correctly identified 83.5% of the false responses. Using the .05 level of significance, is the accuracy of the new polygraph better from the older one?

(a) Use the five steps of hypothesis testing. Explicitly label each of these five steps.

(b) Draw a curve and label the cutoff(s), rejection region(s), and sample’s score.

(c) Provide an interpretation of the finding.

Interpretation: One sentence conclusion of the hypothesis test that should be free of statistical jargon

Answer 1

Only 1 question is done.

7. A nutritionist wants to determine whether people who regularly drink one protein shake per day have different cholesterol levels than people in general. In the general population, cholesterol is normally distributed with μ = 190 and σ = 30. A person followed the protein shake regimen for two months and his cholesterol is 155. Use the 1% significance level to test the nutritionist’s idea.

Step 1 -

Null hypothesis: Mean cholesterol level of people who regularly drink one protein shake per day have the same cholesterol levels than people in general.

Alternate hypothesis: Mean cholesterol level of people who regularly drink one protein shake per day have different cholesterol levels than people in general.

Step 2 -

We shall use a z test and a two tail test. The level of significance is 0.005 ( Since it is a two tail test)

Step 3 - Decision rule

If the test statistic is less than the critical value, we shall reject the null hypothesis.

Or if the pvalue is less than 0.005, we shall reject the null hypothesis.

Step 4

Calculating the z statistic

We use the normal table to find the zcritical for the probability of 0.005.
zcritical = -2.5758

Step 5

Since the zstat > zcritical, we fail to reject the null hypothesis and conclude that the mean cholesterol level of people who regularly drink one protein shake per day have the same cholesterol levels than people in general.
The test results do not support the claim.