In a previous study conducted several years ago, a man owned on average 16 dress shirts. The standard deviation of the population is 3. A researcher wishes to see if that average has changed. He selected a random sample of 41 men and found that the average number of dress shirts that they owned was 15.5. At α=0.10 is there enough evidence to support the claim that the average has changed? Assume that the variable is normally distributed. Use the P -value method with a graphing calculator.
(a) State the hypotheses and identify the claim.
(b) Find the P -value.
(c) Make the decision.
(d) Summarize the results.