[1] Assume that we collect a large (n> 30) simple random sample of annual incomes of adults in the United States. Because the sample is large, can we approximate the distribution of these incomes with a normal distribution? Why or why not? Explain.
[2] Answer the following briefly:
a) What is the purpose of constructing a normal probability plot?
b) If we select a simple random sample of M&M plain candies and construct a normal probability plot of their weights, what pattern would we expect in the plot?
c) Assume that we collect a data set of ages of all San Francisco City Police officers. Examining a histogram and normal probability plot are two different ways to assess the normality of that data set. Identify a third way.
[3] An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from the Physician Insurers Association of America).
a) What is the best point estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed
b) Construct a 98% confidence interval estimate of the proportion of medical malpractice lawsuits that are dropped or dismissed?
c) Does it appear that the majority of such suits are dropped or dismissed?
d) To determine whether the majority of such suits are dropped or dismissed, we perform a hypothesis test. What are the null hypothesis and alternative hypothesis?
H0 (null hypothesis):
H1 (alternative hypothesis):
e) Using a significance level corresponding to the confidence level used in (b), test the claim that the majority of such suits are dropped or dismissed.
Attachment:- Statistics HW_CH.docx