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 = .05.
b. Can you conclude that acupuncture significantly reduces back pain? Use a one-tailed test with = .05.
To find: Whether or not the acupuncture has significant effect on back pain by using two-tailed test at .
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 is performed.
Step 1: Null Hypothesis is and Alternate Hypothesis is
Step 2: For a sample of , the t-statistics will have degrees of freedom, i.e. . For a two-tailed test with and , the critical value (CV) is obtained from the t-table as .
Step 3: t-statistics can be calculated using formula:
First, calculate sample standard deviation, s, using formula:
Substitute and in the formula
To find: Whether or not the acupuncture has significant effect on backpain for one-tailed test at .
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