GM 533 Applied Managerial Statistics Final Exam Answers

(TCO D) PuttingPeople2Work has a growing business placing out-of-work MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample.
Sample size: 100
Population standard deviation: 5
Sample mean: 34.2
Formulate a hypothesis test to evaluate the claim.

(TCO B) Assume that customers patronizing the newly opened Nordstrom’s at River City Mall are binomially distributed by wealth (rich = income greater than \$250,000/year; poor = the rest of us). If 10 people visit the Nordstrom’s on a typical weekend shopping day, determine the following:

Binomial distribution

 10 n 0.5 p

 X P(X) cumulative probability 0 0.00098 0.00098 1 0.00977 0.01074 2 0.04395 0.05469 3 0.11719 0.17188 4 0.20508 0.37695 5 0.24609 0.62305 6 0.20508 0.82813 7 0.11719 0.94531 8 0.04395 0.98926 9 0.00977 0.99902 10 0.00098 1.00000

What is the probability that at least three will be rich?

3. Question : (TCO A) Company ABC had sales per month as listed below. Using the Minitab output given, determine:(A)  Range (5 points);
(B)  Median (5 points); and
(C)  The range of the data that would contain 68% of the results. (5 points).Raw data: sales/month (Millions of \$)
23
45
34
34
56
67
54
34
45
56
23
19

 Descriptive Statistics: Sales Variable Total Count Mean StDev Variance Minimum Maximum Range Sales 12 40.83 15.39 236.88 19.00 67.00 48.00

 Stem-and-Leaf Display: SalesStem-and-leaf of Sales N = 12 Leaf Unit = 1.0 1 1 9 3 2 33 3 2 6 3 444 6 3 6 4 6 4 55 4 5 4 3 5 66 1 6 1 6 7

4. Question : (TCO C, D) Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla’s requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.Descriptive statistics

 count 16 mean 99.850 sample variance 4.627 sample standard deviation 2.151 minimum 96.9 maximum 104 range 7.1 population variance 4.338 population standard deviation 2.083 standard error of the mean 0.538 tolerance interval 95.45% lower 95.548 tolerance interval 95.45% upper 104.152 margin of error 4.302 1st quartile 98.850 median 99.200 3rd quartile 100.550 interquartile range 1.700 mode 103.000

5. Question : (TCO D) A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacturer’s claim, and explain your answer.

 Test and CI for One Proportion Test of p = 0.05 vs p > 0.05 Sample X N Sample p 98% Lower Bound Z-Value P-Value 1 8 100 0.080000 0.024283 1.38 0.084

(TCO B) The following table gives the median incomes of families by level of income and geographical region.

 East South Midwest West Totals <\$80,000/year 102 98 39 62 301 \$80,000 to less than \$250,000/year 263 514 120 351 1248 \$250,000/year or more 100 226 65 99 490 Totals 465 838 224 512 2039

(A) Referring to the above table, if a family is chosen at random, what is the probability that it is either from the South or from the West? (15 points)
(B) Referring to the above table, given that the family is from the Midwest, what is the probability that it has an annual income of at least \$250,000? (15 points)

(TCO B, F) The length of time Americans exercise each week is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes

 X P(X≤x) P(X≥x) Mean Stddev 11 .0146 .9854 15.8 2.2 15 .3581 .6419 15.8 2.2 21 .9910 .0090 15.8 2.2 24 .9999 .0001 15.8 2.2 p(lower) p(upper)

(A) Analyze the output above to determine what percentage of Americans will exercise between 11 and 21 minutes per week. (15 points)
(B) What percentage of Americans will exercise less than 15 minutes? If 1000 Americans were evaluated, how many would you expect to have exercised less than 15 minutes? (15 points)

3. Question : (TCO C) A random sample of 16 Google managers yields the following information on annual salaries. The sample mean is \$89,000, with a sample standard deviation of \$8,000. What is the mean salary of all Google managers? What is the 95% confidence interval for the population mean?One-Sample T

 N Mean StDev SE Mean 95% CI 16 89000 8000 2000 (84737, 93263)

(TCO E and F) The U.S Department of Transportation and Safety performed an analysis to determine safe driving speeds. To obtain information about the safe driving speed, it analyzed data from multiple countries comparing the maximum allowed speed limit to the observed death rate. The analysis revealed the following:

Refer to the Minitab output below to answer questions A through G.

 Regression Equation Death rate (per 100 million vehicles = -0.535979 + 0.0789418 Speed limit (miles per hour) Coefficients Term Coef SE Coef T P 95% CI Constant -0.535979 2.34352 -0.22871 0.825 (-5.94014, 4.86818) Speed limit (miles per hour) 0.078942 0.03849 2.05106 0.074 (-0.00981, 016770)

 Summary of Model S = 0.836621 R-Sq = 34.46% R-Sq(adj) = 26.27% PRESS = 10.8252 R-Sq(pred) = -26.70%

 Analysis of Variance Source DF Seq SS Adj SS Adj MS F Regression 1 2.94453 2.94453 2.94453 4.20687 Speed limit (miles per hour) 1 2.94453 2.94453 2.94453 4.20687 Error 8 5.59947 5.59947 0.69993 Lack-of-Fit 3 3.37947 3.37947 1.12649 2.53714 Pure Error 5 2.22000 2.22000 0.44400 Total 9 8.54400 Source P Regression 0.074385 Speed limit (miles per hour) 0.074385 Error Lack-of-Fit 0.170419 Pure Error Total

 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 4.20053 0.265262 (3.58883, 4.81222) (2.17663, 6.22443)

 Values of Predictors for New Observations New Obs Speed limit (miles per hour) 1 60

(A) Analyze the above output to determine the regression equation. (10 points)
(B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.) (10 points)
(C) What conclusions are possible using the coefficient of determination (r-squared)? (6 points)
(D) Calculate the coefficient of correlation. Interpret this value. (6 points)
(E) Does this data provide significant evidence (a=0.05) that the death rate is associated with the speed limit? Find the p-value and interpret. (6 points)
(F) Determine the average death rate for a speed limit of 60 miles per hour. (6 points)
(G) What is the 95% confidence interval for the death rate for a speed limit of 60 miles per hour? What conclusion is possible using this interval? (6 points)

(TCO E and F) A national trade association is concerned with increasing competition from foreign companies. They decide, in close consultation with their membership, to evaluate the sales performance of 25 randomly selected U.S. companies, so that all companies can benefit from their collective experience.

The association’s research director, with substantial input from member companies’ sales managers, has decided to measure the performance, y, of each company by using the yearly sales of the same product for all of the companies.

The research director and the sales managers believe that sales performance, y (measured in hundreds of units), substantially depends on three independent variables:

x1  = sales of the product and all competing products in the company (Market Potential, in hundreds of units)

x2   = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)

x3  = weighted average of the company’s market share over the previous four years (Market Share)

Refer to the Minitab output below to answer questions A through G.

Multiple Regression and Model Building: Minitab Output

Coefficients

 Term Coef SE Coef T P 95% CI Constant -1603.58 505.550 -3.17195 0.005 (-2654.93, -552.231) Market Potential, x1 0.05 0.007 7.26321 0.000 (0.04, 0.070) Advertising, x2 0.17 0.044 3.78288 0.001 (0.08, 0.260) Market Share, x3 282.75 48.756 5.79927 0.000 (181.35, 384.139)

Summary of Model

 S = 545.515 R-Sq = 84.90% R-Sq(adj) = 82.74% RESS = 8616510 P  R-Sq(pred) = 79.18%

Analysis of Variance

 Source DF Seq SS Adj SS Adj MS F P Regression 3 35130240 35130240 11710080 39.3502 0.0000000 Market Potential, x1 1 14788185 15698916 15698916 52.7542 0.0000004 Advertising, x2 1 10333786 4258521 4258521 14.3102 0.0010905 Market Share, x3 1 10008270 10008270 10008270 33.6315 0.0000093 Error 21 6249309 6249309 297586 Total 24 41379549

Predicted Values for New Observations

 New Obs Fit SE Fit 95% CI 95% PI 1 4251.56 178.023 (3881.34, 4621.78) (3058.22, 5444.90)

Values of Predictors for New Observations

 New Obs Marketing Potential, x1 Advertising, x2 Market Share, x3 1 35182.7 7281.65 9.64

1. Analyze the above output to determine the multiple regression equation. (5 points)
2. What conclusions are possible using the result of the global usefulness test (the F test and its associated p-value)? (5 points)
3. What conclusions are possible using the results of the t-tests of the independent variables (alpha = 0.05). Does this data provide significant evidence that Sales are associated with Market Potential and/or Advertising and/or Market Share?  Find the p-values and interpret. Interpret the 95% confidence interval of each of the regression coefficients, using the units of the variables. (20 points)

Find and interpret the 95% Prediction interval for Sales, when Market Potential = 35182.7, Advertising = 7281.65, and Market Share = 9.64. (10 points)