1. The International Council of Shopping Centers reports that the average teenager spends $39 during a shopping trip to the mall.  The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and teen-appreciation days that feature special bargains for this age group.  He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do.  Mall management decides to evaluate the promotions directo's success by surveying a simple random sample of 45 local teens and finding out how much they spent on their most recent shopping visit to the mall.  The results are listed below.  Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teens in this area might be higher than for US teens as a whole.  Identify and interpret the p-value for the test.  Using the 0.025 level of significance, what conclusion do you reach?

Problem 2: Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches.  As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inches.  For a recent random sample of 34 tubes, the mean diameter was 2.509 inches.

If th e true population mean is real ly 2.520 inches, what is the probability that the inspector will correctly reject the false null hypothesis that the population mean = 2.500 inches?

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