SOLUTION: Problem 3:
a) Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop i
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a) Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop i
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Question 247146: Problem 3:
a) Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another $1 discount on the regular price of a $5 deluxe car wash. Option C is a $2 discount on the same $5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below:
Option A Option B Option C
$453
507
513
521
511
615
601
552
551
505
515
512
476
427 $492
514
536
511
528
678
611
653
596
516
534
543
498
437 $467
525
516
500
435
462
411
674
512
559
624
711
512
416
a) State the null hypothesis to test for equal population means. (5 Points)
b) (5 Points.) Below are the results from EXCEL of ANOVA of the data at the 0.05 level of significance. Do the sample data indicate the at least one of the three population mean total returns is different from the others? Why? (Explain using “F” and “Fcrit” – a drawing is fine.)
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 14 7259 518.5 2555.962
Column 2 14 7647 546.2143 4340.335
Column 3 14 7324 523.1429 8389.209
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 6169 2 3084.5 0.605377 0.550917 3.2381
Within Groups 198711.6 39 5095.168
Total 204880.6 41
Use the following information for questions 5-9 (2 points each).
A consumer research company collected data for 16 models of sport utility vehicles of various sizes. The research team measured the overall fuel economy and the distance between their front and rear axles (wheelbase) of each vehicle. The scatter plot and line of best fit is shown in the diagram below.
5. Which one of the following statements concerning the regression line is true?
a. There is a positive linear relationship between the two variables.
b. The slope is greater that 1.
c. The intercept is at or near 30.
d. Vehicles with larger wheelbases have the worst fuel economy.
6. The slope of the regression line, b1, is at or near which of the following values?
a. –0.3
b. 0
c. 0.3
d. 3
7. The intercept of the regression line, b0, is at or near which of the following values?
a. 20
b. 30
c. 60
d. 160
8. Juanita Douglas just bought a new red SUV that has a wheelbase of 115 inches. What overall fuel economy can she expect to obtain?
a. 28 mpg
b. 25 mpg
c. 20 mpg
d. 15 mpg
9. A –0.947 correlation coefficient has been found between two variables after examining 43 pairs of observations. What can be concluded?
a. There is a strong positive relationship between the two variables.
b. There is a strong negative relationship between the two variables.
c. There is a weak positive relationship between the two variables.
(