1. Sandy James thinks that housing prices have stabilized in the past few months. To convince her boss, she intends to compare current prices with last years prices. She collects 12 housing prices from the want ads: 125,900 216,000 158,100 251,000 189,000 241,000 208,000 116,200 182,000 214,000 272,800 150,700 She then calculates the mean and standard deviation of the prices she has found.

What are these two summary values?

2. A large construction company is trying to establish a useful way to view typical profits from jobs obtained from competitive bidding. Because the jobs vary substantially in size and the final amount of the successful bid, the company has decided to express profits as percent earnings: Percent earnings = 100 · Earnings Actual construction costs When money is lost on a project, the earnings are negative and so is the resulting net profit. A sample of 30 jobs yields these percent earnings:

15.9

21.3

-1.8

6.6

0.4

53.6

19.7

-0.5

6.7

-2.3

11.9

-0.3

19.0

12.8

-9.6

26.8

21.0

32.0

-0.4

10.9

6.9

-8.5

3.5

3.5

-1.9

4.0

13.0

15.1

9.7

33.9

a. Calculate an estimate of the mean percent earnings for the population of jobs.

b. Construct a 95% confidence interval for the mean percent earnings for the population of jobs treating 30 as a large sample size.

c. Construct a 95% confidence interval for the mean percent earnings for the population of jobs treating 30 as a small sample size (hint: to calculate the correct cutoff, use the function TINV in Excel).

d. Comparing your answers in parts b and c, explain why 30 is often used as the cutoff when labeling samples as “large” or “small.”

3. From data on a large sample of sales transactions, a small business owner reports that a 95% confidence interval for the mean profit per transaction, µ, is (43.6, 105.9). Use these data to determine:

a. A point estimate (best guess) of the mean, µ.

b. A 90% confidence interval for the mean, µ.

4. To better assess your willingness-to-pay for advertising on others websites, you want to learn the mean profit per visit for all visits to your website. To accomplish this, you have collected a random sample of 4,738 visits to your website over the past six months. This sample includes information on visit duration and profits. The data are contained in webprofits.xlsx.

a. Using the data in webprofits.xlsx, build a 99% confidence interval for the mean profit per visit for all of your visitors.

b. Let the null hypothesis be that mean profit per visit for all of your visitors is $11.50.

i. Calculate the corresponding t-stat for this null hypothesis.

ii. Calculate the corresponding p-value for this null hypothesis.

iii. With strength of 95%, decide whether or not to reject this null hypothesis.

iv. Detail the reasoning behind your decision