John, an experienced Airbnb host claims that true average rental price per night for a shared room in lower east side of Manhattan is $100. A sample of n=15 shared room rentals from the neighborhood yields a sample average price per night of $85 with a standard deviation $17 (source: Kaggle.com).

Suppose the distribution of price per night is normally distributed. Is there sufficient evidence to believe that average price per night for a shared room in Manhattan's lower east side is less than what John claims? (Use 5% significance level)?

1. Clearly state the null and alternative hypothesis to answer the above research question. Define any parameters you may use.
2. Check the conditions that needs to be satisfied in order to do the test you stated in part 1.
3. Calculate the test statistic
4. Calculate the p value for the test. You may use MINITAB to get the numerical value of the p value. However, you MUST clearly state the p value as a probability statement.
5. What is the rejection region for the test?
6. Write the final conclusion in the context of the problem.