Suppose you want to test a new natural supplement that is marketed as having cog

Question

Suppose you want to test a new natural supplement that is marketed as having cognitive benefits. To test the supplement, you design an experiment: 40 students are recruited and administered a math test. Then, they take the supplement daily for one month; at the end of this period, they take another math test again. The tests have similar problems of the same difficulty, but they are not identical to avoid retest bias. After all the data has been collected, you want to test if the pre-supplementation scores are significantly different from the post-supplementation scores. You are a skeptic, so you do not believe the supplement is strictly beneficial- in other words, you believe it may improve scores, but my also lower them.

Write the null and alternative hypothesis for this problem. Define all symbols used.

What test would you use?

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: d = 0

Alternative hypothesis: d 0 (Where Before - After = d )

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.

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