An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the miles per gallon of the automobile. The following data is collected:
X
50
55
55
60
60
62
65
65
Y
28
26
25
22
20
20
17
15
   •   In the space below, use technology to construct a scatterplot of the bivariate data set.




   •   What is the value for r? Interpret this value, would you say that the correlation is positive or negative? Strong or Weak? How do you know?



   •   From the regression equation given above, what value is the slope of the line? Interpret this slope, what does it tell us about the relationship between average speed and miles per gallon?

   •   Predict the miles per gallon of a car traveling 63 miles per hour.

   •   Predict the average speed of a car whose fuel mileage is 23 miles per gallon.


(f) Find r squared. What does this statistic tell us about between average speed and miles per gallon?


1. Many people in the small town of Econville have complained that there is no park for children to use afterschool. There are 20 households in the town, 10 who have children and 10 who do not. The households with children value the park being built at $100 each while the other households value it at $20 each. The town estimates that the cost of building a park is $600. All households earn the same income.

   1. (a) Would describe the park as a public good? Explain.

   2. (b) The first proposal is fund the park with a flat tax. What is the minimal tax per household required to build the park? Who will and who will not support such a tax and will the park be built?

   3. (c) A second proposal is a tax that only applies to the households with children. What tax per household will ensure that the park is built? Who will and who will not support such a tax? Why?

   4. (d) Athirdproposalisataxpaymentthatisproportionaltothebenefiteachhousehold receives from the park. In this proposal, how much will each household be expected to pay? Who will and who will not support such a tax? Why?

   5. (e) Evaluate the three policies listed and state which you will choose and why.

Marigold Industries purchased a truck at the beginning of 2020 for $109300. The truck is estimated to have a salvage value of $3200 and a useful life of 117000 miles. It was driven 21000 miles in 2020 and 29000 miles in 2021. What is the depreciation expense for 2021?

The probability of A is 0.7, the probability of B is 0.8. What are the possible values for the probability of both A and B happening?

A metropolitan transportation authority has set a bus mechanical reliability goal of 3800 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3850 bus miles and a sample standard deviation of 275 bus miles. Complete parts​ (a) and​ (b) below.

a. Is there evidence that the population mean bus miles is more than 3800 bus​ miles? (Use a 0.05 level of​ significance.)

State the null and alternative hypotheses.

Find the test statistic for this hypothesis test.

The critical​ value(s) for the test statistic​ is(are):

Is there sufficient evidence to reject the null hypothesis using alpha=0.05​?

b. Determine the​ p-value and make a conclusion.

The p-value is:

What is the conclusion for this test? Reject or Do not reject the null hypothesis.

A car company claims that its new SUV gets better gas mileage than its competitor’s SUV. A random sample of 35 of its SUVs has a mean gas mileage of 12.6 miles per gallon (mpg). The population standard deviation is known to be 0.4 mpg. A random sample of 31 competitor’s SUVs has a mean gas mileage of 12.4 mpg. The population standard deviation for the competitor is known to be 0.3 mpg. Test the company’s claim at the 0.05 level of significance.

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles; the sample standard deviation was 1,412 miles. To determine if the spark plugs average 22,100 miles, what is the critical value for the test using a 0.05 level of significance?

A) t = +2.110

B) t ≠ ±2.110

C) t = -2.110

D) t = ±2.110

Select the taxpayer who meets the distance requirement for deducting moving expenses. A)Bill's new workplace is half a mile from his old home. His old home is 60 miles form his old workplace. B) Connie's new workplace is five miles from her old home. Her old home is two miles from her old workplace. C)Danica just completed U.S. Air Force basic training and is moving to her first duty station. D) Yuri's new workplace is 65 miles from his old home. His old home is 25 miles from his old workplace.

You know that there is a problem in your car due to sounds you hear when driving. There can be only two sources for the problem 1) Brakes 2) Engine. You are estimating that the problem is due to brakes with probability 0.6, and it is due to engine with probability 0.4. Furthermore, if the problem is due to brakes or engine, the number of miles you can drive without any repair is exponentially distributed with mean 500 and 100 miles, respectively.

a) What is the probability that the number of miles you can drive the car without any repair is larger than 200 miles.?

b)What is the expected number of miles you can drive the car without any repair?