Question

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 u = 190 and o = 30. A person followed the protein shake regimen for two months and his cholesterol is 135. Use the 1% significance level to test the nutritionist's idea. (a) Use the five steps of hypothesis testing.

Expert Please Answer

Population 1:

Population 2:

N= __________

(b) Draw a curve and label the cutoff -2.33, rejection region(s), and sample's score.

f) what is the approximate comparison distribution (the population distribution, or the sampling distribution, why?

g) Is a one tailed or two tailed test appropriate in this situation, and why?

Answer 1

Population 1: General population of people who do not regularly drink one protein shake per day

Population 2: People who regularly drink one protein shake per day

Step 1: Specify the Hypothesis

Null hypothesis H0: People who regularly drink one protein shake per day have same average cholesterol levels as people in general whose average cholesterol is 190.

Alternative hypothesis Ha: People who regularly drink one protein shake per day have different average cholesterol levels than people in general whose average cholesterol is 190.

Step 2: Specify the Test.

Since we know the population standard deviation of cholesterol levels of general population, we will conduct one sample z test.

Step 3: Set the Significance Level and critical value

The significance level is 1% or 0.01

Since we are testing for both cases, whether people who regularly drink one protein shake per day have less or greater average cholesterol levels than people in general, this is a two-tailed test. The critical value of z for two-tailed tests are

-2.58 and 2.58

We reject null hypothesis H0 if Sample z score < -2.58 or > 2.58

Step 4: Calculate the Test Statistic

Test statistic, z = (Sample mean - u) / o

= (135 - 190)/30

= -1.83

Step 5: Drawing a Conclusion

Since the sample test statistic does not lie in the rejection region, we fail to reject the null hypothesis H0 and conclude that there is no significant evidence that people who regularly drink one protein shake per day have different average cholesterol levels than people in general whose average cholesterol is 190

(b)

The rejection region is shown in gray and the sample's score is -1.83 shown in blue dot.

(f)

The approximate comparison distribution follows Normal distribution because by Central Limit Theorem the general population cholesterol is normally distributed with u = 190 and o = 30

(g)

Since we are testing for both cases, whether people who regularly drink one protein shake per day have less or greater average cholesterol levels than people in general, this is a two-tailed test.