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31. (4 points (bonus)) Use the following information to answer the question. A research company developed a drug to help lung cancer patients live longer. Without treat- ment, the average life expectancy for lung cancer patients is 3.2 months. The research company claim that their drug help cancer patients live longer. Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: Ho: μ =3.2 and Ha: μ > 3.2. The research company randomly select 33 patients with lung cancer and gave them their drug. The sample mean was 3.3 months with a sample standard of 1 month. Find the critical value (t) for this problem. deviation 32. (4 points (bonus) When do we use the t-distribution versus the z-distribution? 33. (4 points (bonus) If the test statistics is 1.47 and the critical value is 1.697 for a right tail test, should the research reject H0 or should they fail to reject Ho.
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