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##### Final exam 2014

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Question;Page 1;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.;0;1;2 or more;Total;Low;Risk;56;22;8;86;Medium;Risk;18;40;12;70;High;Risk;11;13;20;44;Total;85;75;40;200;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 Maryland 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);Page 2;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);Page 2;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 %).;RETURN;FOOTAGE;PREDICT;18.3;12.8;15.0;11.7;18.6;7.5;19.5;10.3;17.5;14.3;15.4;14.2;9.8;21.4;11.4;18.6;14.5;16.7;16.3;15.5;19.0;9.8;17.0;14.2;15.1;16.2;19.5;12.8;10.9;19.4;16.3;15.0;16.3;15.4;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 7.5Correlations;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);Question 1. 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.;SALES;TEMP;PRICE;P-TEMP;P-PRICE;3;72;200;75;190;4;77;200;7;82;150;1;43;200;0;31;200;0;28;200;8;81;140;5;83;200;5;76;200;4;60;185;4;50;190;5;55;190;Correlations;SALES, TEMP, PRICE;SALES TEMP;TEMP;0.849;0.000;PRICE;-0.736 -0.435;0.006 0.158;Cell Contents;Pearson correlation;P-ValueGeneral;Regression Analysis: SALES versus TEMP, PRICE;Regression Equation;SALES = 9.02846 +;0.0822089 TEMP - 0.0545506 PRICE;Coefficients;Term Coef;SE;Coef T;P 95% CI;Constant 9.02846 3.37308 2.67662 0.025;(1.39801, 16.6589);TEMP 0.08221;0.01569 5.24111 0.001 (0.04673, 0.1177);PRICE -0.05455 0.01505;-3.62424 0.006 (-0.08860, -0.0205);Summary of Model;S =;0.936302 R-Sq =;88.67% R-Sq(adj) = 86.16%;PRESS =;11.4214 R-Sq(pred) = 83.61%;Analysis of Variance;Source DF Seq;SS Adj SS Adj;MS F P;Regression;2 61.7767 61.7767 30.8884 35.2341 0.0000554;TEMP 1;50.2617 24.0812 24.0812 27.4692 0.0005340;PRICE;1 11.5151 11.5151 11.5151 13.1351 0.0055351;Error 9 7.8900 7.8900 0.8767;Total 11;69.6667;Fits and Diagnostics;for Unusual Observations;Obs SALES Fit SE;Fit Residual St Resid;12 5;3.18533 0.285747 1.81467 2.03522 R;R denotes an;observation with a large standardized residual.;Predicted Values for;New Observations;New;Obs Fit SE;Fit 95%;CI 95%;PI;1 4.82951 0.353065 (4.03082, 5.62819);(2.56586, 7.09315);Values of Predictors;for New Observations;New;Obs TEMP PRICE;1 75 190;a. Analyze the above output to determine the multiple regression equation.;b. Find and interpret the multiple index of determination (R-Sq).;c. Perform the t-tests on,(use two tailed test with (a=.05). Interpret your results.;d. Predict the sales for an individual week a mean temperature of 75 and a;price of $190. Use both a point estimate and the appropriate interval estimate.;(Points: 31)

Paper#61350 | Written in 18-Jul-2015

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