Question

In an experiment designed to test the effectiveness of paroxetine for treating bipolar depression, subjects are measured using the Hamilton Depression Scale with the results below[1]. 43 patients were used in the placebo group; the sample mean was 21.57 and the sample standard deviation was 3.87. The treated group had 33 patients, a sample mean of 20.38 and s = 3.91. A lower score is better. 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

Assumption and conditions: Samples should be simple random samples. Sample should be independent.

Since sample sizes are large so no need to assume that populations are normally distributed.

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Confidence interval:

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Hypothesis test is:

Conclusion: We cannot conclude that treatment is effective. Since we fail to reject the null hypothesis so type II error is possible.