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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher for a cereal company wanted to demonstrate the health of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30-day period, cholesterol was measured for each individual. Then the participants began a second 30-day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30-day period, cholesterol levels were measured again and the researcher recorded the difference between the two scores for each participant. For this sample, cholesterol scores averaged MD = 16 points lower with the oatmeal with SS = 538 for the difference scores.

a. Are the data sufficient to indicate a significant change in cholesterol level? Use a two-tailed test with α = .01.

b. Compute r2, the percentage of variance accounted for by the treatment, to measure the sire of the treatment effects.

c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

a.

To determine
The sufficiency of data to indicate that there is significance change in the cholesterol level using two tail tests.

Explanation

Given info:

The average of student MD is 16, SS is 538 and n is 9.

Calculation:

The null hypothesis:

H0:μD=0  (There is no difference between the two tests)

The alternative hypothesis:

H1:μD0  (There is difference between the two tests)

The sample variance:

s2=SSn1

s2=53891=5388=67.25

Thus, the sample variance is 67.25.

The standard deviation of the mean:

sMD=s2n

sMD=(67

b.

To determine
The coefficient of the determination.

c.

To determine
The Cohen’s d to measure the size of the effect.

To describe: About the result of hypothesis test and the measure of effect of size.

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