1) Suppose we have a random sample of twenty-two communities. From this sample, we computed an average of = 121.3 reported cases of larceny per year with a standard deviation of 37.3 cases per year. Find an 85%, 90%, and 95% confidence interval for the population mean annual number of reported larceny cases in such communities.

a.) 85% CI:

b.) 90% CI:

c.) 95% CI:

2) 2.)] In a random sample of 81 professional actors, it was found that 8 were extroverts. Let p represent the proportion of all actors who are extroverts.

a.) What variable do we use for the point estimate for p?

b.) Find the point estimate for p.

c.) What variable do we use for the point estimate for q?

d.) Find the point estimate for q.

e.) If you wanted to find a 95% confidence interval, would you use a normal distribution critical value (0.95) or a Student's t distribution critical value (0.95) to calculate the maximal margin of error (E)?

2) In a random sample of 61 professional actors, it was found that 22 were extroverts. Find a 95% confidence interval for p.

3) A random sample of medical files is used to estimate the proportion p of all people who have blood type B. If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 99% sure that the point estimate will be within a distance of 0.07 from p?