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4. A farmer wants to check whether the median weight of pumpkins from his jumbo patch is different from 16. Let M be the population median, and use hypotheses Ho : M = 16 versus HA : M # 16 and use significance level a = 0.05. (a) Compute the observed test statistic and p-value for the following sample of 9 jumbo pumpkins: 12.6, 12.9, 14.8, 14.3, 15.9, 19.1, 10.2, 11.4, 9.3 Draw a conclusion in the context of the problem. (b) Discuss how the statistical decision made in (a) compares to your intuitive impression about the amount of evidence against the null that the sample contained. (c) Explain how, if at all, your observed test statistic and p value for the hypothesis test would change if the 19.1 1b pumpkin had actually been 35 lbs. 5. An electric car companys sales manager wants to assess the affordability of electric vehicles. Specif- ically, he is interested in learning about the salaries of of people who are on the wait list for the company's most affordable model. He sent a survey to a random sample of 2000 of the people on the wait list. 85 of the respondents reported having salaries below $100,000, 103 reported having salaries above, and the rest of the surveys were not returned. (a) Why should the car companys sales manager be cautious about applying the results of this survey to all salaries of people on the waitlist? (hint: think about the data collection). What population can the manager more confidently make inference about? (b) Carry out and interpret a z proportion test (with a = 0.05) of the hypotheses Ho : p = 0.5 versus HA : P + 0.5 (after checking relevant assumptions) where p is the proportion of the population identified in (a) with salaries above $100,000. (c) Construct a 95% confidence interval for p using a z CI. Compare this interval to your results in part (b)