Stan Moneymaker has been shopping for a new car. He is interested in a certain? 4-cylinder sedan that averages

29 miles per gallon. But the sales person tried to persuade Stan that the? 6-cylinder model of the same automobile only costs $2,500 more and is really a? "more sporty and? responsive" vehicle. Stan is impressed with the zip of the?6-cylinder car and reasons that ?$2,500 is not too much to pay for the extra power. How much extra is Stan really paying if the? 6-cylinder car averages 20 miles per? gallon? Assume that Stan will drive either automobile 103,000

?miles, gasoline will average ?$3.17 per? gallon, and maintenance is roughly the same for both cars. State other assumptions you think are appropriate.

a) Identify the claim: state the null and alternative hypotheses. b) Determine the test: left-tailed, right-tailed, or two-tailed. c) Identify the degree of freedom and determine the critical value. d) Graph your bell-shaped curve and label the critical value. e) Find your standardized test statistic ? and label it on your graph. f) Decide whether to reject or fail to reject the null hypothesis. g) Interpret your result.

A trucking firm suspects that the mean life of a certain tire it uses is less than 35,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,350 miles with a standard deviation of 1200 miles. At α = 0.05, test the trucking firm's claim.

Moana is a sailing from her home to a nearby island which is 215 miles north and 33 miles west. There is a constant ocean current of 0.50 knots moving from west to east. Moana can sail her boat at a cruising speed of 5.5 miles per hour in still water.

1. What angle should Moana sail to get to the island?

2. How long will it take her to get there?

3. Moana’s friend Maui is floating on a raft that is moving with the ocean current (meaning, he is not traveling with respect to the water). Would Maui see Moana’s boat traveling with a speed faster than, slower than, or equal to what an observer standing on the shore would see? Explain your reasoning

Use the data given in the table to answer the following questions. The data represents the average number of miles that a salesperson travels in a day verses the number of sales made each month.

(a) What is the value of the correlation coefficient for this set of data? Round to 3 decimal places.

(b) What is the equation of the Regression Line for this set of data? Round values to two decimal places.

(c) Predict the number of sales an associate could expect to make if he travelled an average of 108 miles each day. Round to two decimal places.

Data are gathered on each car in the motor pool, regarding number of miles (in thousand miles) driven in a given year, and maintenance costs (in thousand dollars) for that year:

Part of the linear regression analysis output are shown in below:

3. Construct a 95% confidence interval for the conditional mean of y given x0=50.

   (A) [2.476, 2.879]   (B) [1.538, 2.409] (C) [1.651, 2.30] (D) [2.410, 2.908]

3. Construct a 95% prediction interval at x0=50.

(A) [2.360, 2.996]

(B) [2.064, 3.254]

(C) [1.612, 2.335]

(D) [2.223, 3.132]

Boston Railroad decided to use the high-low method and operating data from the past six months to estimate the fixed and variable components of transportation costs. The activity base used by Boston Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved. Transportation Costs Gross-Ton Miles January $530,900 224,000 February 591,900 250,000 March 418,300 162,000 April 567,500 242,000 May 476,000 195,000 June 610,200 263,000 Determine the variable cost per gross-ton mile and the total fixed cost. Variable cost (Round to two decimal places.) $ per gross-ton mile Total fixed cost $

Whenever you are asked to test a hypothesis, be sure to: (a) state the null and alternative hypotheses; (b) state the relevant sample statistic; (c) give the rejection region; (d) compute the test; (e) give your decision and a conclusion in English.

1. Assume that last year, licensed American drivers drove an average of 10,000 miles, with a standard deviation of 2,000 miles (these are population figures). This year, the government campaigned to get people to save gas by driving less. To test the effectiveness of the campaign, a study is conducted. A sample of 100 drivers is drawn at random from the general population and the number o fmiles driven by each person is recorded. On the average, these 100 drivers drove 11,000 miles. Was the campaign effective? Use alpha = .01.

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

Required:

Use the step method to allocate the service costs, using the following:

The order of allocation starts with Maintenance. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

b. The allocations are made in the reverse order (starting with Cafeteria). (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

Two trains of equal weight, moving with velocities of 30 miles an hour each and in opposite directions collide. Show that the loss of energy caused by the impact is the same as in the case of a train moving at 60 miles an hour striking another at rest. In the latter case, find the velocity with which the debris will be moved along the track. Also show that before impact the total energy in the one case is doubled that in the other

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