The New York Stock Exchange recently reported that the average age of a female shareholder is 44 years. A broker in Chicago wants to know whether this figure is accurate for the female shareholders in Chicago. The broker secures a master list of shareholders in Chicago and takes a random sample of 58 women. Suppose the average age for shareholders in the sample is 45.1 years, with a population standard deviation of 8.7 years. Test to determine whether the broker’s sample data differ significantly enough from the 44-years figure released by the New York Stock Exchange to declare that Chicago female shareholders are different in age from female shareholders in general. Use α = .05. If no significant difference is noted, what is the broker’s probability of committing a Type II error: (Round the intermediate values to 3 decimal places. Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)
a. If the average age of a female Chicago shareholder is actually 45 years?
b. If the average age of a female Chicago shareholder is actually 46 years?
c. If the average age of a female Chicago shareholder is actually 47 years?
d. If the average age of a female Chicago shareholder is actually 48 years?
e. Construct an OC curve for these data.
f. Construct a power curve for these data.