MATH 533 Final Exam

MATH 533 Final Exam

Question 1. 1. (TCO E) McCave Development Enterprises is considering whether to build a shopping mall in Statesville. The manager wants you to analyze the relationship between mall size and the rate of return on invested capital. You select a random sample of 16 cities similar to Statesville in demographic and economic characteristics and collect the following data on FOOTAGE (in 10,000 square feet) and RETURN (rate of return as a %).

Q2) Correlations: RETURN, FOOTAGE
 
Pearson correlation of RETURN and FOOTAGE = -0.954
P-Value = 0.000

a. Analyze the above output to determine the regression equation.
b. Find and interpret βˆ1in the context of this problem.
c. Find and interpret the coefficient of determination (r-squared).
d. Find and interpret coefficient of correlation.
e. Does the data provide significant evidence (a = .05) that Footage can be used to predict Return? Test the utility of this model using a two-tailed test.  Find the observed p-value and interpret.
f.  Find the 95% confidence interval for the mean rate of return on capital investment for malls that have square footage of 150,000. Interpret this interval.
g. Find the 95% prediction interval for the rate of return on capital investment for a mall that has square footage of 150,000. Interpret this interval.
h. What can we say about the rate of return on capital investment for a mall that has square footage of 75,000?
  (Points : 48)

1. (TCO E) The manager of a retail outlet suspects that sales of air conditioners are associated with the price of the air conditioners, as well as the mean temperature. Twelve weeks are selected at random. The results are found in the MINITAB printout below.

1. (TCO A) Consider the following age data, which is the result of selecting a random sample of 22 Boeing 747 airplanes that are owned by United Airlines. The age of each airplane is given in years.

17         5          5          12         8          5          8          16         14         12         22
15         5          8          17         5          4          2          22         17         20         23

3. Compute the mean, median, mode, and standard deviation, Q₁, Q₃, Min, and Max for the above sample data on age of Boeing 747 airplanes owned by United Airlines.
   b. In the context of this situation, interpret the Median, Q₁, and Q₃. (Points : 33)

2. (TCO B) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below.

If you choose a tire at random, then find the probability that the tire

a. was made by Michelin.
b. was made by Goodyear and was defective.
c. was not defective, given that the tire was made by Bridgestone. (Points : 18)

3. (TCO B) A source in the Internal Revenue Service has stated that historically 90% of federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are selected and checked carefully for arithmetic errors. Assuming independence, find the probability thata. all 25 returns are free of arithmetic errors.
   b. at most 23 returns are free of arithmetic errors.
   c. more than 17 are free of arithmetic errors. (Points : 18)

4. (TCO B) Fuel efficiency for cars made in the United States is normally distributed with a mean of 28.8 mpg and a standard deviation of 8.2 mpg.a. What percentage of cars made in the United States have fuel efficiency above 40 mpg?
   b. What percentage of cars made in the United States have fuel efficiency between 25 and 35 mpg?
   c. A special tax credit is planned for the best (highest) 8% of cars made in the United States in terms of fuel efficiency. How high must the fuel efficiency be in order to qualify for this special tax credit? (Points : 18)

5. (TCO C) The manufacturer of batteries used in small electrical appliances wants to estimate the average life of a battery. A random sample of 12 batteries yields the following results.Sample Size = 12
   Sample Mean = 34.2 hours
   Sample Standard Deviation = 5.9 hoursa. Construct the 90% confidence interval for the average life of a battery.
   b. Interpret this interval.
   c. How many batteries should be sampled if we wish to generate a 90% confidence interval for the average life of a battery that has a margin of error of 1 hour? (Points : 18)

7. (TCO D) A contract dispute between the National Football League and the Player’s Association arose regarding the retirement system. The NFL agreed to a settlement only if it could be shown convincingly that less than 60% of the players retired with 5 years or less playing time in their careers. A random sample of 200 retired NFL players is selected with 116 having played for 5 years or less. Does the sample data provide evidence to conclude that the percentage of players retiring with 5 years or less of playing time is less than 60% (using a = .01)?a. Formulate the null and alternative hypotheses.
   b. State the level of significance.
   c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
   d. Compute the test statistic.
   e. Decide whether you can reject Ho and accept Ha or not.
   f. Explain and interpret your conclusion in part e.  What does this mean?
   g. Determine the observed p-value for the hypothesis test and interpret this value.  What does this mean?
   h. Does this sample data provide evidence (with a = .01), that the percentage of players retiring with 5 years or less of playing time is less than 60%? (Points : 24)

8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results.Sample Size = 144
   Sample Mean = $66,124
   Sample Standard Deviation = $7,400Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using a = .05)? Use the hypothesis testing procedure outlined below.a. Formulate the null and alternative hypotheses.
   b. State the level of significance.
   c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
   d. Compute the test statistic.
   e. Decide whether you can reject Ho and accept Ha or not.
   f. Explain and interpret your conclusion in part e. What does this mean?
   g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
   h. Does the sample data provide evidence to conclude that the population mean annual household income is in?

6. (TCO C) An auditor for the U.S. Postal Service wants to examine its special Two-Day Priority mail handling to determine the proportion of parcels that actually require longer than 2 days for delivery. A randomly selected sample of 100 such parcels is found to contain seven that required longer than 2 days for delivery.a. Compute the 90% confidence interval for the population proportion of parcels that require longer than 2 days for delivery.
   b. Interpret this confidence interval.
   c. How large a sample size will need to be selected if we wish to have a 90% confidence interval that is accurate to within 1%? (Points : 18)