Solve the following problem:
Q1: A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day.
Use the .01 significance level.
(1) This a -tailed test. Drop down options: one or two
(2) The decision rule is to reject H0 μr ≥ μd if Z <
(3) The test statistic is Z
(4) What is your decision regarding ?
(5) The p-value is .
Q2: The management of Discount Furniture, a chain of discount furniture stores in the North-east, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.
Salesperson Before After
Sid Mahone $320 $340
Carol Quick 290 285
Tom Jackson 421 475
Andy Jones 510 510
Jean Sloan 210 210
Jack Walker 402 500
Peg Mancuso 625 631
Anita Loma 560 560
John Cuso 360 365
Carl Utz 431 431
A. S. Kushner 506 525
Fern Lawton 505 619
Hint: For the calculations, assume the "After" data as the first sample.
(1) State the decision rule for .05 significance level: H0: d â?¤ 0; H1: d> 0.
(2) Compute the value of the test statistic.
(3) Compute the p-value.
(4) Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the 0.05 significance level.
H0. There is increase in the typical salesperson's weekly income due to the innovative incentive plan.
Q3: The president of the American Insurance Institute wants to compare the yearly costs of auto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured driver, others with several teenage drivers, and pays each family a stipend to contact the two companies and ask for a price quote. To make the data comparable, certain features, such as the amount deductible and limits of liability, are standardized. The sample information is reported below.
At the .10 significance level, can we conclude that there is a difference in the amounts quoted? Hint: For the calculations, assume the Progressive Car insurance as the first sample.
Family Progressive
Car Insurance GEICO Mutual
Insurance
Becker $2,090 $1,610
Berry 1,683 1,247
Cobb 1,402 2,327
Debuck 1,830 1,367
DuBrul 930 1,461
Eckroate 697 1,789
German 1,741 1,621
Glasson 1,129 1,914
King 1,018 1,956
Kucic 1,881 1,772
Meredith 1,571 1,375
Obeid 874 1,527
Price 1,579 1,767
Phillips 1,577 1,636
Tresize 860 1,188
Reject H0 if z < or z > .
The test statistic is
Decision: