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| m484 | Great Plains Roofing and Siding Company Inc. sells roofing and siding products to home repair retailers, such as Lowe’s and Home Depot, and commercial contractors. The owner is interested in studying the effects of several variables on the value of shingles sold ($000). The marketing manager is arguing that the company should spend more money on advertising, while a market researcher suggests it should focus more on making its brand and product more distinct from its competitors.
The company has divided the United States into 26 marketing districts. In each district, it collected information on the following variables: volume of sales (in thousands of dollars), advertising dollars (in thousands), number of active accounts, number of competing brands, and a rating of district potential.
Conduct a multiple regression analysis to find the best predictors of sales.
a. Draw a scatter diagram comparing sales volume with each of the independent variables. Comment on the results.
b. Develop a correlation matrix. Do you see any problems? Does it appear there are any redundant independent variables?
c. Develop a regression equation. Conduct the global test. Can we conclude that some of the independent variables are useful in explaining the variation in the dependent variable?
d. Conduct a test of each of the independent variables. Are there any that should be dropped?
e. Refine the regression equation so the remaining variables are all significant.
f. Develop a histogram o |
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| m485 | Grills Video Products purchases LCDs from Mira Electronics. According to his sampling plan, Art Grills, owner of Grills Video, will accept a shipment of LCDs if 3 or fewer are defective in a sample of 25. Develop an OC curve for these percents defective: 10%, 20%, 30%, and 40%. You will need a statistical software package. |
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| m486 | A group of 10,000 people are tested for a gene called Ifi202 that has been found to increase the risk for lupus. The random variable is the number of people who carry the gene. |
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| m487 | Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
Pounds Overweight Frequency
0 up to 6.......... 14
6 up to 12.......... 42
12 up to 18.......... 58
18 up to 24......... 28
24 up to 30.......... 8 |
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| m488 | hen only two treatments are involved, ANOVA and the Student’s t test (Chapter) result in the same conclusions. Also, t2 = F. As an example, 14 randomly selected Introduction to History students were divided into two groups, one consisting of 6 students and the other of 8. One group took the course in the normal lecture format. The other group of 8 students took the course via the Internet. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups.
Traditional Lecture Internet
19 ............. 32
17 ............. 28
23 ............. 31
22 ............. 26
17 ............. 23
16 ............. 24
27
25
a. Using analysis of variance techniques, test H0 that the two mean test scores are equal; α = .05.
b. Using the t test from Chapter 11, compute t.
c. Interpret the results. |
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| m489 | Here is a table showing the number of employed and unemployed workers 20 years or older by gender in the United States.
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and thewomen. |
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| m490 | Historically, Widgets Manufacturing Inc. produces 250 widgets per day. Recently the new owner bought a new machine to produce more widgets per day. A sample of 16 days’ production revealed a mean of 240 units with a standard deviation of 35. Construct a confidence interval for the mean number of widgets produced per day. Does it seem reasonable to conclude that the mean daily widget production has changed? Justify your conclusion. |
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| m491 | Horwege Electronics Inc. purchases TV picture tubes from four different suppliers. Tyson Wholesale supplies 20% of the tubes, Fuji Importers 30%, Kirkpatricks 25%, and Parts Inc. 25%. Tyson Wholesale tends to have the best quality, as only 3% of its tubes arrive defective. Fuji Importers’ tubes are 4% defective, Kirkpatricks’ 7%, and Parts Inc.’s are 6.5% defective.
a. What is the overall percent defective?
b. A defective picture tube was discovered in the latest shipment. What is the probability that it came from Tyson Wholesale? |
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| m492 | Hugger Polls contends that an agent conducts a mean of 53 in-depth home surveys every week. A streamlined survey form has been introduced, and Hugger wants to evaluate its effectiveness. The number of in-depth surveys conducted during a week by a random sample of 15 agents are:
At the .05 level of significance, can we conclude that the mean number of interviews con-ducted by the agents is more than 53 per week? Estimate thep-value. |
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| m493 | Human Resource Consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $502 with a standard deviation of $100.
a. Compute the standard error of the sample mean for HRC.
b. What is the chance HRC finds a sample mean between $477 and $527?
c. Calculate the likelihood that the sample mean is between $492 and $512.
d. What is the probability the sample mean is greater than $550? |
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| m494 | IBM Inc. is going to award a contract for fine-line pens to be used nationally in its offices. Two suppliers, Bic and Pilot, have submitted bids. To determine the preference of office employees, brokers, and others, a personal preference test is to be conducted using a randomly selected sample of 20 employees. The .05 level of significance is to be used.
a. If the alternate hypothesis states that Bic is preferred over Pilot, is the sign test to be conducted as a one-tailed or a two-tailed test? Explain.
b. As each of the sample members told the researchers his or her preference, a “1” was recorded if it was Bic and a “2” if it was the Pilot fine-line pen. A count of the pluses revealed that 12 employees preferred Bic, 5 preferred Pilot, and 3 were undecided. What is n?
c. What is the decision rule in words?
d. What conclusion did you reach regarding pen preference? Explain. |
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| m495 | If Ί: Rn -> Rn is a norm preserving linear transformation and M is a k-dimensional manifold in Rn, show that M has the same volume as Ί(M). |
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| m496 | If A, B, and C are mutually exclusive events with P(A) = 0.2, P (B) =0.3, and P(C) = 0.4, determine the following probabilities:
(a) P (A U B U C)
(b) P (A ∩ B ∩ C)
(c) P (A ∩ B)
(d) P [(A U B) ∩ C]
(e) P (A’ ∩ B’ ∩ C’) |
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| m497 | If A, B, and C are mutually exclusive events, is it possible for P (A) = 0.3, P (B) = 0.4, and P (C) = 0.5? Why or why not? |
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| m498 | If A = [a1, b1] x . x [an, bn] and f: A -> R is continuous, define f: A -> R by |
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| m499 | If C is a bounded set of measure 0 and ∫ AXC exists, show that ∫ AXC = 0. |
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| m500 | If f: A ->R is integrable, show that |f| is integrable and |f A f| <f A |f| |
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| m501 | If f: [a, b] x [c, d] -> R is continuous and D2f is continuous, define F (x, y) = ∫xa (t,y) dt
a. Find D1F and D2F.
(b) If G (x) = ∫ g(x) f (t, x) dt, find G1 (x). |
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| m502 | If f: A->R is non-negative and ∫ Af = 0, show that B = {x: f (x) ≠ 0} has measure 0. |
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| m503 | If f: R2->R and D2f =0 and D2f =0, show that f is independent of the second variable. If D1f = D2f =0, show that f inconstant. |
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