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Eight people with high blood cholesterol have changed their diets to avoid foods high in cholesterol, such as meats and dairy products. After two months on this diet, their cholesterol levels are re-measured.  The following data are changes in their cholesterol levels in mg/dL (=final measure –initial measure): -40             -27                  14                    -8        -31          10         -38           -26 a. Test the hypothesis that consuming a low cholesterol diet for two months affects blood cholesterol levels. (Hint: if there is a difference, then the change won’t be equal to zero.) Follow the 4 steps of hypothesis testing, stating your null and alternative hypothesis in symbols, and giving a complete finding in plain English with detailed statistical notation.b. Now test the hypothesis that consuming a low cholesterol diet for two months decreases blood cholesterol levels by 10 mg/dL. Again, show all 4 steps. (Hint: remember that a null hypothesis of “no difference” can be “not different from a particular value.”)

Question

Eight people with high blood cholesterol have changed their diets to avoid foods high in cholesterol, such as meats and dairy products. After two months on this diet, their cholesterol levels are re-measured.  The following data are changes in their cholesterol levels in mg/dL (=final measure –initial measure):

 

-40             -27                  14                    -8        -31          10         -38           -26

 

a. Test the hypothesis that consuming a low cholesterol diet for two months affects blood cholesterol levels. (Hint: if there is a difference, then the change won’t be equal to zero.) Follow the 4 steps of hypothesis testing, stating your null and alternative hypothesis in symbols, and giving a complete finding in plain English with detailed statistical notation.

b. Now test the hypothesis that consuming a low cholesterol diet for two months decreases blood cholesterol levels by 10 mg/dL. Again, show all 4 steps. (Hint: remember that a null hypothesis of “no difference” can be “not different from a particular value.”)

check_circleAnswer
Step 1

a.

Test whether consuming a low cholesterol diet for two months affects blood cholesterol levels:

Paired or dependent samples:

Any two randomly selected samples are said to be paired, if each observation in one sample is paired with the observation in the second sample.

Here, the final measures and initial measures are collected on the same sample of 8 people with high blood cholesterol levels.

Therefore, the observations of the initial measures sample can be paired with the observations of the final measures sample.

Since, the samples are dependent, paired sample t test is appropriate.

Let μd be the population mean difference between the final measure and initial measure.

The objective is to test whether the population mean difference between the final measure and initial measure is equal to “0” or not.

The hypotheses are given below:

Null hypothesis:

H0 : μd = 0

That is, the population mean difference between the final measure and initial measure is equal to 0.

Alternative hypothesis:

H1 : μd ≠ 0(Two tail test).

That is, the population mean difference between the final measure and initial measure is not equal to 0.

Step 2

Obtain the mean and standard deviation of the difference between the final measure and initial measure:

Excel procedure to find the mean and standard deviation of differences:

Step 1: Enter the values of difference between final measure and initial measure from A2:A9.

Step2: Obtain the mean of difference in cell B10, by entering the formula “=AVERAGE(A2:A9)”.

Step3: Obtain the standard deviation of difference in cell B11, by entering the formula “=STDEVA(A2:A9)”.

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Step 3

Obtain the test statistic value.

The sample mean of difference between the final measure and initial measure is d – bar = –18.25 and the sample standard deviation of difference between the final measure and i...

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