7.63 Simulate a sampling distribution The table (data are available on the book’s website) provides prices per night for all 51 available hotel rooms (as of December 2014) in Panama City Beach, Florida, for a week in March 2015

(spring break). The distribution of these prices is characterized by m = $196 and s = $57.4.

a. Each student or the class should construct a graphical display (stem-and-leaf plot, dotplot, or histogram)
of the population distribution of the prices.
(Alternatively, access the Sampling Distribution for the Sample Mean web app available on the book’s website. Select Build Own for the shape and copy and paste the prices in the text field. This provides a smoothed graph for the population distribution of hotel prices, with m = 196 and s = 60.)

b. Each student should select nine random numbers between 1 and 51, with replacement (e.g., using random.org). Using these numbers, each student should sample nine hotels and find the mean price for these hotels. Collect all sample mean prices.
Using technology, construct a graph (using the same graphical display as in part

a) of the simulated sampling distribution of the x-values for all the student samples. Compare it to the distribution in part a.
(Alternatively, you can simulate taking random samples of size 9 with the sampling distribution web app under the setting mentioned in part a.)

c. Find the mean of the x-values in part

b. How does it compare to the value you would expect in a long run of repeated samples of size 9?

d. Find the standard deviation of the x-values in part b.
How does it compare to the value you would expect in a long run of repeated samples of size 9?

Hotel Price St. Thomas Square 75 American Quality Lodge 92 Hathaway Inn 105 Top Of The Gulf 129 Palm Grove 134 Shores of Panama 139 Sleep Inn 140 La Quinta 155 Beachside Resort 156 Hawthorn Suites 159 Origin Beach 159 The Reef 159 Casa Loma 163 Sunbird Beach 165