Question: The present success rate in the treatment of a particular psychiatric disorder is 0.65 (65%). A research group creates a new treatment for this disorder. Their null hypothesis is that the success rate for the new treatment is 0.65 (no different from the standard). The alternative hypothesis is that the success rate is better than 0.65 for the new treatment.

1. Let p = true success rate of the new treatment. Using statistical notation, write null and alternative hypotheses about p .
2. A clinical trial is done in which 144 of 200 patients who use the new treatment are successfully treated.
   What is the value of \[\hat{p}\] = success rate for the sample? How does it compare to 0.65 (the old standard)?
3. In Minitab use Stat>Basic Stats>1 proportion , click Summarized Data , enter 200 for number of trials and 144 for Number of events. Click on Perform Hypothesis Test and enter 0.65 where it says "Hypothesized proportion" AND click Options to select the alternative hypothesis as "greater than" AND also click on "Use test and interval based on normal distribution."
   What value is given for the test statistic in the output? _______ What is the p -value? ______
4. Decide between the null hypothesis and the alternative hypothesis. Explain your decision.
5. Write a conclusion about how the new treatment compares to previous treatment(s).
6. Suppose the data had been that 50 patients used the new treatment, with 36 successes. What is the value of \[\hat{p}\] = success rate for this sample? How does it compare to the success rate for the sample used in parts b-e?
7. With the data given in part f, use Minitab to do a hypothesis test of whether the "true" success rate for the new treatment is not or is greater than .65. That is, repeat part c but change the number of trials and events to 50 and 36 respectively.
   What value is given for the test statistic in the output? _______ What is the p -value? ______
8. Refer to the previous two parts. Decide between the null hypothesis and the alternative hypothesis. Explain your decision.
9. For the trial with only 50 patients (and 36 success), write a conclusion about how the new treatment compares to previous treatment(s).
10. Briefly explain what this activity illustrates about how sample size affects the statistical significance of an observed result. As a starting points, note that the observed success rate was .72 for both samples, and we wish to determine if this is "significant" evidence that the true proportion is greater than .65.

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