Question: A dietician sets up a test of significance for his weight loss supplement. Individuals are randomly assigned to either the treatment (supplement) group or control (placebo) group. To test the hypothesis that the supplement causes weight loss, the dietician calculates:

d = average _control — average _treatment

Assume that at the start of the experiment d = 0, so we only need to consider the value of d at the end of the trial.

1. After 6 months, the dietician calculates d. What should the null and alternative hypotheses be in terms of d? Null: there’s no real difference. It is just chance. Alternative: there’s a real difference (not just chance).
2. Suppose that d = 10 lbs and the standard error for d is given by SE(d) = 7.5. What is the p-value in the dietician’s experiment? Please show your calculation process.
   test statistic = 1.333 P value = 0.091
3. Provide an interpretation of the p-value obtained in the previous part (i.e. what does a p-value of 0.091 mean?) There’s a 0.091 chance of observing a difference of d = 10 or more extreme, assuming the null is true.
4. If you find a p-value of 0.091 what conclusion can you make assuming a significance level of 5%? At a 5% significance level, we fail to reject the null hypothesis. The difference seems to be explained just by chance.
5. The dietician wants to find significant results, so he repeats the experiment 20 times with his significance level set to 0.05. In the first 19 trials, he finds p > 0.05. The p-value on trial 20 was 0.04. He claims that the final experiment shows that his results are significant. Do you agree with the dietician’s interpretation? Please provide an explanation . At a 5% significance level, the final experiment shows a significant p-value (0.04). However, taking into account the previous 19 results, the observed difference in the last experiment can be explained by chance. 1 out of 20 is 0.05; assuming that the null hypothesis is true, we expect to have 5% experiments in which the results seem to be significant, while in reality it's just random error.

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