Question

People spend about $5 billion annually in the USA for the purchase of magnets used to treat a wide variety of pain. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale (a higher score indicates less pain), and the results of the study are obtained below[1].   The magnet was used for 20 patients, resulting in a sample mean of 0.49 and a sample standard deviation of 0.96. Also, 20 patients treated with a non-magnetized look-alike instrument, giving a sample mean of 0.44 and a sample standard deviation of 1.44. Go through “The Drill” for independent t-tests (Use a 0.05 α-level and the corresponding confidence interval.)

The Drill:

Assumptions and Conditions

Distribution of the sample mean

Mechanics – computing the confidence interval.

Interpretation in context .

Meaning of “We are 95% confident ….”

Margin of error given the confidence interval.

Compute a sample size given a margin of error (and other parameters). (1-prop z only)

Assumptions and Conditions (if any additional)

One or two-sided?

α-level

Statement of the Hypothesis

Distribution of the sample mean under Ho.

(Make a picture)3 !

Mechanics – test statistic

p-value

Interpretation in context

Conclusion

Type I and Type II error (taught in Chapter 19.)

Answer 1

Assumptions and Conditions: Samples are simple random sample and independent. The populations are normally distributed.

Since confidence interval contains zero so we cannot conclude that there is a significant difference between pain scores of two treatments.

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Conclusion;

There is no evidence to conclude that there is a significant difference between pain scores of two treatments.

Since we fail to reject the null hypothesis to type II error is possible.