Final exam 2014

Question 1. 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

a. 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)

Question 2. 2.(TCO B) Consider the following data on new customers for AJ Auto Insurance, specifically the information of the risk level of the customer and the number of tickets they have had in the last year.

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

a. low risk.
b. low risk and had two or more tickets in the last year.
c. medium risk, given that the customer had zero tickets in the last year. (Points : 18)

Question 3. 3.(TCO B) According to a survey by the Opinion Research Corporation, 60% of all clerical workers in the United States “liked their jobs very much.” A random sample of 15 clerical workers is selected. Find the probability that

a. exactly nine of these clerical workers “liked their jobs very much.”
b. at least seven of these clerical workers “liked their jobs very much.”
c. fewer than five of these clerical workers “liked their jobs very much.” (Points : 18)

Question 4. 4.(TCO B) A study of homeowners in the 5th congressional district in found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research).

a. What percentage of household incomes are greater than $30,000?
b. What percentage of household incomes are between $25,000 and $40,000?
c. If an advertising campaign is to be targeted at those whose household incomes are in the top 20%, find the minimum income level for this target group? (Points : 18)

Question 5. 5.(TCO C) The Ford Motor Company wishes to estimate the mean dollar amount of damage done to a Ford Explorer as a result of a 10 mph crash into the rear bumper of a parked car. The sample results are as follows.

Sample Size = 36
Sample Mean = $638
Sample Standard Deviation = $115

a. Construct a 95% confidence interval for the average dollar amount of damage.
b. Interpret this interval.
c. How large a sample size will need to be selected if we wish to have a 95% confidence interval for the average dollar amount of damage with a margin for error of $10? (Points : 18)

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Question 6. 6.(TCO C) A clock company is concerned about errors in assembly of their custom made clocks. A random sample of 120 clocks from today’s production yields nine clocks with assembly errors.

a. Compute the 95% confidence interval for the percentage of clocks with assembly errors in today’s production.
b. Interpret this confidence interval.
c. How many clocks should be selected in order to be 95% confident of being within 2% of the population percentage of clocks with assembly errors in today’s production? (Points : 18)

Question 7. 7.(TCO D) According to Information Resources Inc., based on sales of teeth-cleaning products, Crest toothpaste controlled a 31.2% share of the market. A researcher from a rival company believes that this figure is high, and that in fact, Crest controls less than 31.2% of the market. A simple random sample of 400 consumers yields 116 use Crest. Does the sample data provide evidence to conclude that the researcher from the rival company is correct (witha = .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 Crest’s market share is below 31.2% (witha = .05)? (Points : 24)

Question 8. 8.(TCO D) A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars gives the following result.

Sample Size = 81
Sample Mean = 4.97%
Sample Standard Deviation = 1.8%

Does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars (usinga = .10)? 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 dealership averages more than 4.5% profit on sales of new cars (usinga = .10)? (Points : 24)

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 %).

Regression Analysis: RETURN versus FOOTAGE

The regression equation is
RETURN = 30.0 - 0.943 FOOTAGE


Predictor Coef SE Coef T P
Constant 29.976 1.238 24.22 0.000
FOOTAGE -0.94257 0.07921 -11.90 0.000


S = 0.969721 R-Sq = 91.0% R-Sq(adj) = 90.4%


Analysis of Variance

Source DF SS MS F P
Regression 1 133.15 133.15 141.59 0.000
Residual Error 14 13.17 0.94
Total 15 146.31


Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 15.838 0.244 (15.315, 16.360) (13.693, 17.982)
2 22.907 0.666 (21.479, 24.334) (20.384, 25.429)X

X denotes a point that is an outlier in the predictors.


Values of Predictors for New Observations

New Obs FOOTAGE
1 15.0
2 7.5


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 interpretin 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)