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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

A researcher is investigating the effectiveness of acupuncture treatment for chronic back pain. A sample of n = 4 participants is obtained from a pain clinic. Each individual ranks the current level of pain and then begins a 6-week program of acupuncture treatment. At the end of the program, the pain level is rated again and the researcher records the amount of difference between the two ratings. For this sample, pain level decreased by an average of M = 4.5 points with SS = 27.

a. Are the data sufficient to conclude that acupuncture has a significant effect on back pain? Use a two-tailed test with α = .05.

b. Can you conclude that acupuncture significantly reduces back pain? Use a one-tailed test with α = .05.

a.

To determine

To find: Whether or not the acupuncture has significant effect on back pain by using two-tailed test at α=0.05.

Explanation

Given info:

A sample of 4 individuals is selected from a population. The sample mean and sum of squared difference (SS) is found to be 4.5 and 27 respectively. Two-tailed hypothesis test using α=0.05 is performed.

Calculations:

Step 1: Null Hypothesis is H0:μD=0 and Alternate Hypothesis is H1:μD0

Step 2: For a sample of n=4, the t-statistics will have (n1) degrees of freedom, i.e. df=3. For a two-tailed test with α=0.05 and df=3, the critical value (CV)  is obtained from the t-table as t=±3.182.

Step 3: t-statistics can be calculated using formula:

t=Mμsm

First, calculate sample standard deviation, s, using formula:

s=SSn1

Substitute SS=27 and n=4 in the formula

s=2741=273=9

b.

To determine

To find: Whether or not the acupuncture has significant effect on backpain for one-tailed test at α=0.05.

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