A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

Use Excel - no hand calculations.

1. Write the regression equation.

2. Interpret the regression constant and regression coefficient.

3. Forecast a value for the dependent variable, test the significance of the regression coefficient at an alpha level of .05

4. Test the overall significance of the regression model, and Interpret the coefficient of determination.

Rio Bus Tours has incurred the following bus maintenance costs during the recent tourist season. (The real is Brazil’s national monetary unit. On the day this exercise was written, the real was equivalent in value to .269 U.S. dollar.)

Required:

1. Use the high-low method to estimate the variable cost per tour mile traveled and the fixed cost per month.

2. Develop a formula to express the cost behavior exhibited by the company’s maintenance cost.

3. Predict the level of maintenance cost that would be incurred during a month when 44,000 tour miles are driven.

A tire manufacturer is interested in testing the fuel economy for two different tread patterns. Tires of each tread type were driven for 1000 miles on each of 9

different cars. The mileages, in miles per gallon, were as follows:

(a) Construct an 80% confidence interval for the mean difference in fuel economy. Let d represent the mileage of tread pattern A minus the mileage of tread B. Use tables to find the critical value and round the answers to at least two decimal places.

A high school guidance counselor is interested in the relationship between proximity to school and participation in extracurricular activities. He collects the data on distance from home to school (in miles) and number of clubs joined for a sample of 10 juniors. Using the following data, compute a Pearson’s correlation coefficient and indicate whether the correlation is significant. State your null and alternative hypothesis and show your work step by step. Make sure interpret your finding (Use .05 significance level).

Which best illustrates the distinction between statistical significance and practical importance?

Multiple Choice

• "In 2016, 240 out of 400 statistics students at Oxnard Technical College sold their textbooks at the end of the semester, compared with 220 out of 330 students in 2015, a significant decrease."

• "Our new manufacturing technique has increased the life of the 80 GB USB AsimoDrive external hard disk significantly, from 240,000 hours to 250,000 hours."

• "In 50,000 births, the new vaccine reduced the incidence of infant mortality in Morrovia significantly from 14.2 deaths per 1000 births to 10.3 deaths per 1000 births."

• "The new Sky Penetrator IV business jet’s cruising range has increased significantly from 3,975 miles to 4,000 miles."

Which best illustrates the distinction between statistical significance and practical importance?

Multiple Choice

• "In 2016, 240 out of 400 statistics students at Oxnard Technical College sold their textbooks at the end of the semester, compared with 220 out of 330 students in 2015, a significant decrease."

• "Our new manufacturing technique has increased the life of the 80 GB USB AsimoDrive external hard disk significantly, from 240,000 hours to 250,000 hours."

• "In 50,000 births, the new vaccine reduced the incidence of infant mortality in Morrovia significantly from 14.2 deaths per 1000 births to 10.3 deaths per 1000 births."

• "The new Sky Penetrator IV business jet’s cruising range has increased significantly from 3,975 miles to 4,000 miles."

1. If you decrease the level of confidence from 99% to 95%, the width of confidence interval will A. increase by 4% B. decrease by 4% C. decrease by 8% D. None of the above

2. If you wish to decrease the margin of error, you may do which one of the following: A. Increase the sample size. B. Reduce the population size. C. Decrease the level of confidence.

D. Both b and c  E. Both a and c

3. In five test runs, a truck operated 10, 12, 10, 8, and 15 miles with one gallon of gasoline. At the 98% level of confidence, is this sufficient evidence to show that the truck is operating at a mean rate of about 14 miles per gallon? A. Yes. B. No. C. Can’t be determined. D. Depends on the proportion of the tested truck

The action plan in the Boston Bike Network Plan anticipates spending $30 million in construction costs for work on establishing and renovating 100 miles of bike lanes in the city. The overall goal of the Boston Climate Action Plan is to reduce vehicle miles traveled (VMT) by 5.5% from 2005 levels, which would result in an estimated reduction of 68 thousand tons of CO2 per year. Assume the bike paths and VMT effects last for 30 years, the value of CO2 reduction is $40 per ton (based on another study), and the discount rate is 5%. In years 10 and 20, 10% of the original capital cost is spent for maintenance.

a. Calculate the B/C ratio, net present value, and internal rate of return for the bike path network.

1. What is the Coefficient of Determination?
   1. 0.7334
   2. 0.4053
   3. 0.2267
   4. 0.1437
2. What is the Test Statistic for the Correlation Coefficient?
   1. 3.32
   2. 16.15
   3. 1.88
   4. Cannot be computed
3. What is the regression slope?
   1. 1.98
   2. 0.40
   3. 0.71
   4. 0.32
4. What is the regression intercept?
   1. 0.40
   2. 2.41
   3. 3.68
   4. 1.88
5. If a salesman travels 600 miles what is the predicted sales?
   1. $4826
   2. $2105
   3. $3638
   4. $4018
6. Given a Correlation of Coefficient of 0.42, what is the ratio of SSR/SST?
   1. 0.00
   2. 0.42
   3. 0.48
   4. 0.18
7. A regression equation is computed to be: Y = 15.8 + 11.2X.
   We know the corresponding SST = 685 and SSR = 282. What is the correlation coefficient?
   1. 0.83
   2. 0.41
   3. 0.64
   4. Cannot be computed from data available

A random sample of 20 workers in a factory were asked to report the age of their car and how many miles the vehicle had on it. A computer printout resulted in the following information.

1. Find the LSRL
2. A new worker starts next week and we know that his car is 7 years old, how many miles would you expect to be on his car?
3. Interpret the slope of the LSRL in the context of this problem.
4. Find a 95% confidence interval for the slope of the LSRL
5. Without calculating it what do you know about an 85% confidence interval compared to your answer in part b?