A fire insurance company thought that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 4.7 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they thought, would convince the insurance company to lower its rates. They randomly identified 64 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 4.4. If σ = 2.4 miles, does the sample show sufficient evidence to support the community's claim at the α = 0.05 level of significance?

A.) Conduct a hypothesis test using the classical approach.

B.) Conduct a hypothesis test using the p-value approach.

1. You live 20 miles away from your job, where you work five days per week (except for a two-week vacation every year). Your car gets 35 miles per gallon, on average.
   1. If the average price per gallon of gas is $2.50, how much should you budget for gas for your commute in your annual budget?
   2. You are considering a new job that is 30 miles from where you live. How much more will your commute cost you each year?
   3. If you take the new job and the price of gas rises to $3.00 per gallon, how much more will your commute cost you each year?

A fire insurance company thought that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 4.7 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they thought, would convince the insurance company to lower its rates. They randomly identified 64 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 4.4. If σ = 2.4 miles, does the sample show sufficient evidence to support the community's claim at the α = 0.05 level of significance?

A.) Conduct a hypothesis test using the classical approach.

B.) Conduct a hypothesis test using the p-value approach.

Continental 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 Continental Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved.

Determine the variable cost per gross-ton mile and the total fixed cost.

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.