Zillow.com reported that the mean value per square foot for homes in the Phoenix, Arizona, area dropped from $172 in 2006 to $66 in 2011 (source: zillow.com/local-info/AZ-Phoenix-Metro-home-value/). Suppose you now intend to draw a sample of 49 homes. You plan to compute the mean value per square foot for the sample. If the current mean value for the population of houses in the Phoenix area is $86 per square foot and the standard deviation is $14.
a. Sketch a graph of the sampling distribution that would assign probabilities to the various values that your sample mean could take on.
b. What is the probability that the sample mean you compute will be within 1.96 standard deviations (that is, within ±1.96σx–) of the overall Phoenix area mean.
c. It is 95% likely that the sample mean will be some-where between $____ and $____. (Make your interval symmetric around the population mean.)
d. It is 99% likely that the sample mean will be some-where between $____ and $____. (Make your interval symmetric around the population mean.)