Quantitative Method

All the questions have to be answered manually, no SPSS answers will be accepted. 

Chapter 18

18.2       James Jesse, the head of the Bureau of Animal Husbandry, perceives that several agencies received large increases in appropriations last year because they encouraged interest groups to testify for them before the House Appropriations Committee. The accompanying sample data for five agencies similar to Jesse’s were gathered. Using regression analysis, calculate a regression equation. Does a relationship exist? The Bureau of Animal Husbandry could pressure 15 groups to testify for it. What percentage increase in appropriation would this number of groups predict? Place a 90% confidence interval around that estimate. How large an increase is each additional interest group worth?

18.6          Caretakers, a local nonprofit organization, operates the concession stands for the Newland Baseball Park, home of the Newland Nuggets (a minor league baseball team). Doing so permits Caretakers to raise funds to operate its soup kitchen. Caretakers is concerned with waste in the concessions area. Too many precooked hot dogs are left over after a game. Heinz Canine, Caretakers’ research analyst, feels that hot dog consumption (and other concession sales) can be predicted by the number of advance sale tickets purchased for a game (attendance is usually twice advance sales). Heinz gathers the accompanying data for a sample of 10 days. Run the regression for Heinz and tell him whether his hypothesis is correct. Predict how many hot dogs will be sold if 1,000 advance tickets are sold.

Chapter 19

19.2       Graph each set of data shown in the accompanying table. Determine whether the relationships are linear or nonlinear. If nonlinear, state what type of relationship it is.

19.8          The Intercity Bus Company is concerned with the high cost of fuel. The company believes that fuel is being wasted because drivers are exceeding the speed limit. A series of tests (N = 85) shows the following relationship between bus speed (X ) and miles per gallon of fuel (Y ) for speeds between 35 and 85 miles per hour (mph):

Y^ = 12.4 – .11X      s_b = .007  S_y|x = .41  r² = .98

X = 50    s_x = 15

Intercity is considering placing a governor on all buses, limiting their speed to 55 mph. At an average speed of 55 mph, how many miles per gallon would a bus get? Place a 95% confidence limit around this estimate.

Chapter 20

20.2     The Indiana State Department of Agriculture is concerned about the number of acres of farmland being withdrawn from farming. The department would like to propose new legislation to prevent this but would like to show the legisla- ture what would happen if it does not act. Dewey Compost, the department’s statistician, regresses the number of acres used for farming in the state on time 11949 5 year 12. Dewey finds the following:

Y^ 5 2.743 2 .027X

s_b =.0007   S_y|x =.013   r² =.89   s_x =16   X=29  n=63

(a) How strong is the relationship?

(b) If Y is in millions of acres, how many acres of farmland will be lost in the next 10 years if the legislature does not act and if past practices continue?

(c) How many acres will be used for farming in 2012? Place a 90% confidence interval around this estimate.

Chapter 21

21.2 If Janice Position-Classification, personnel officer for the Bureau of Forms, can forecast agency separations 6 months from now, she can plan recruitment efforts to replace these people. Janice believes that separations 6 months from now are determined by the number of agency people passed over for promotion (X₁), the number of agency people 64 years old or older (X₂),  and the ratio of government salaries to private sector salaries (X₃). Using regression, Janice finds the following:

Y^ = 27.4 + .35X₁ + .54X₂ – 271X₃

s_b1 = .0031 s_b2 = 0.136 s_b3 = 263 S_y|x = 54

R² = .89 Adj. R² = .85 N = 214

Write a one-page memo explaining the results, and then forecast the number of separations if 418 people are passed over for promotion, 327 people are 64 years old or older, and government salaries equal those in the private sector.

21.4 The McKeesport Fire Department wants to know how likely it is that a truck pump will fail. The fire chief, George Pyro (no relation), thinks pump failure is a function of age (X₁) and water hardness (X₂ measured on a scale of 1 to 10). The department statistician runs a regression on a dummy variable (coded 1 for failure and 0 for no failure) for 217 pumps. She finds the following:

Y^ = .14 + .01X₁ + .05X₂

s_b1 = .0002 s_b2 = .025 S_y|x = .04 R² = .93 Adj. R² = .92

Write a memo explaining what the regression means. If the average water hardness is 3 and the chief would like to replace any pump with a probability of failing of .80 or more, at what age should pumps be replaced?

1- A political candidate, Bill McWaffle, is personally indifferent on the issue of the legalization of gambling in his state and to this point has not taken a public stand. The election is fast approaching, and he has decided that he will adopt a public stand if at least 65 percent of his constituents feel one way on the issue. Unless there is at least a 65/35 percent split in opinion, he will not take a public stand for fear of alienating a large segment of voters. A random sample of 200 voters shows that 68 favor legalization and 132 oppose. If he wants to be 99 percent certain that at least 65 percent of his constituents feel one way about the issue before he takes a public position, what should he do?

2- Colonel George “Gung” Ho, executive officer of the 101st Ranger battalion, is concerned about whether or not military information on injuries incurred in parachute jumps is inaccurate. The official figures state that there will be 3.9 injuries per 100 jumps. Colonel Ho thinks this figure is suspect especially for night time jumps. To check this out, he randomly selects 150 paratroopers and makes a night jump just outside Panama City. Twelve paratroopers are injured in the jump. Present a hypothesis, a null hypothesis, and evaluate the hypothesis.