Question: You may need to find an apartment to rent upon graduation. The Internet is a valuable source of data to aid you in your search. From neighborhood safety to available transportation to housing costs, recent data can steer you in the right direction. On a Web site, San Mateo County in California published extensive descriptive statistics from its 1998 Quality of Life Survey. The county reported that the mean house payment (mortgage or rent) was $1225.15, with a standard deviation of $777.50. It also reported that the mean cost of an apartment rental, rather than a house rental or a mortgage, was $868.86. For this exercise, treat the overall mean housing payment as a parameter, and treat the mean apartment rental cost as a statistic based on a sample of 100.
a. Using symbolic notation and formulas (where appropriate), determine the mean and the standard error for the distribution of means for the overall housing payment data.
b. Using symbolic notation and the formula, calculate the z statistic for the cost of an apartment rental.
c. Why is it likely that the z statistic is so large?
d. Why is it permissible to use the normal curve percentages associated with the z distribution even though the data are not likely normally distributed?