Statistics - Hypothesis Testing Projects

Chapter 10 62. Refer to the Real Estate data, which reports information on the homes sold in Denver, Colorado,

Chapter 10

62. Refer to the Real Estate data, which reports information on the homes sold in Denver, Colorado, last year.

A recent article in the Denver Post indicated that the mean selling price of the homes in the area is more than $220,000. Can we conclude that the mean selling price in the Denver area is more than $220,000? Use the .01 significance level. What is the p -value?
Determine the proportion of homes that have a pool. At the .05 significance level, can we conclude that less than 40 percent of the homes sold in the Denver area had a pool? What is the p -value?

Chapter 11

52. Refer to the Baseball 2002 data, which reports information on the 30 Major League Baseball teams for the 2002 season.

At the .05 significance level, can we conclude that there is a difference in the mean salary of teams in the American League versus teams in the National League?
34. One reads that a business school graduate with an undergraduate degree earns more than a high school graduate with no additional education, and a person with a master’s degree or a doctorate earns even more. To investigate we select a sample of 25 mid-level managers of companies with less than 200 employees. Their incomes, classified by highest level of education, follow.
High School Undergraduate Master’s Degree

or Less Degree or More
45 49 51
47 57 73
53 85 82
62 73 59
39 81 94
43 84 89
54 89 89
92 95
62 73
Test at the .05 level of significance that there is no difference in the arithmetic mean salaries of the three groups. If the null hypothesis is rejected, conduct further tests to determine which groups differ.
Chapter 13
48. Mr. William Profit is studying companies going public for the first time. He is particularly interested in the relationship between the size of the offering and the price per share. A sample of 15 companies that recently went public revealed the following information.

Company	x (Size, in $ millions)	y (Price per share)
1	9	10.8
2	94.4	11.3
3	27.3	11.2
4	179.2	11.1
5	71.9	11.1
6	97.9	11.2
7	93.5	11
8	70	10.7
9	160.7	11.3
10	96.5	10.6
11	83	10.5
12	23.5	10.3
13	58.7	10.7
14	93.8	11
15	34.4	10.8

Determine the regression equation.

Determine the coefficient of determination. Do you think Mr. Profit should be satisfied with using the size of the offering as the independent variable?

Chapter 14

24. Many regions along the coast in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has resulted in many of the large grocery store chains building new stores in the region. The Kelley’s Super Grocery Stores, Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.

Family	Food	Income	Size
1	5.04	73.98	4
2	4.08	54.9	2
3	5.76	94.14	4
4	3.48	52.02	1
5	4.2	65.7	2
6	4.8	53.64	4
7	4.32	79.74	3
8	5.04	68.58	4
9	6.12	165.6	5
10	3.24	64.8	1
11	4.8	138.42	3
12	3.24	125.82	1
13	6.6	77.58	7
14	4.92	171.36	2
15	6.6	82.08	9
16	5.4	141.3	3
17	6	36.9	5
18	5.4	56.88	4
19	3.36	71.82	1
20	4.68	69.48	3
21	4.32	54.36	2
22	5.52	87.66	5
23	4.56	38.16	3
24	5.4	43.74	7
25	4.8	48.42	5

Food and income are reported in thousands of dollars per year, and the variable "Size" refers to the number of people in the household.

a. Develop a correlation matrix. Do you see any problems with multicollinearity?

b. Determine the regression equation. Discuss the regression equation. How much does an additional family member add to the amount spent on food?

c. What is the value of R 2? Can we conclude that this value is greater than 0?

d. Would you consider deleting either of the independent variables?

e. Plot the residuals in a histogram. Is there any problem with the normality assumption?

f. Plot the fitted values against the residuals. Does this plot indicate any problems with homoskedasticity?

Chapter 15

22. The Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported on the next page.

Number of Applications	Credit Frequency (In days)
0	55
1	77
2	81
3	48
4	31
5 or more	13

To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level. Hint: To find the expected frequencies use the Poisson distribution with a mean of 2.0.

Find the probability of exactly one success given a Poisson distribution with a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner.

28. A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.

Pension Plan

Job Class Plan A Plan B Plan C