Question: The following is a list of the statistical methods we have learned in this course.

#1 Histogram #5 One sample z test #8 Confidence interval

#2 Box-and-whisker plot #6 One sample t test #9 Correlation coefficient

#3 Normal distribution #7 Sampling distribution #10 Linear regression model

#4 Probability of two events

For each of the situations in parts (a) – (d), select the method that you think is the most applicable. No calculation is necessary for all parts.

? If the method you select is a hypothesis test (i.e., Method #5 or #6). State the null and alternative hypotheses (state them in terms specific to the situation, e.g., "mean monthly return of IBM stock is greater than 2%", rather than in general terms like "At > 0.02").

? If the method you select is not a hypothesis test (i.e., Method #1 – #4 or #7 – #10), state briefly what you would look for to address the need of the situation.

(a) Christopher is considering purchasing an apartment near Central Park. He wants to find out whether the closer an apartment is to Central Park, the more expensive it is. He has collected the sales price and the distance to Central Park for 60 recently sold apartments.

(b) Amy is the CEO of a fashion advertising company. She is interesting in finding out if there is sufficient evidence that women on average spend more than $200 per month on clothing. She has the monthly expenditures on clothing of 1,000 randomly selected women.

(c) Patricia plans to invest in Microsoft stock. Based on the monthly returns of Microsoft stock in the last 10 years, she wants to find an estimate that has a 99% chance of covering the true mean monthly return of Microsoft stock.

(d) Tom works for a telemarketing company that tries to sell a product to low-income families in Brooklyn. From a research report Tom learned that the annual incomes for the families in Brooklyn have a mean of $35,000 and a standard deviation of $28,000. Tom needs to randomly call up 100 families in the next few days to promote the product. How should Tom find the probability that these 100 families have an average annual income below $30,000?