Question: To construct a 90% confidence interval for the proportion (percentage) of homes in your state that have an advertised selling price of over $300000, we first need an estimate for the population proportion.

a. Using your original (untrimmed) sample, state the value of p-hat. (See the table constructed in Part 6 of your spreadsheet in order to help you calculate p-hat.)

p is read p-hat.

(Notice the hat "^" on top of the letter p, although it should be directly on top instead of so high above the letter p, indicates that this is the sample proportion of successes.)

b. Using the value you calculated for p-hat for your state, are n times p-hat and n times q-hat both greater than or equal to 5? Note that n is your sample size.

c. If your answer to part b is yes, then construct the 90% confidence interval for p, the population proportion of homes in your state that have an advertised selling price of over $300,000. If your answer to part b is no, then you cannot use the normal distribution to approximate the binomial distribution, but please try constructing the CI using the normal distribution to ensure that you understand how to construct a confidence interval even though the interval that you will construct in this case, using the normal distribution when the normal distribution is not appropriate, is misleading and considered a misuse/abuse of statistics.

d. Write an interpretation (that is, determine a reasonable inference and prediction that then could be used to make appropriate decisions) for the confidence interval you constructed in the context of the prices.