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##### stats problems with solution fall 2014

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Question;1.(TCO E) A sample of 15 computers reveals the following data;in years of service (X1, YEARS), whether the computer is a MAC or not (X2;1=Mac computer, 0=not a Mac computer), and the total number of breakdowns (Y;BREAKDOWNS). The results are found below.;YEARS;MAC;BREAKDOWNS;1;1;0;1;0;1;2;1;0;2;0;2;2;1;1;2;0;3;3;1;1;3;0;4;4;1;2;4;0;5;4;0;6;5;1;3;5;0;7;6;0;8;Correlations: YEARS, MAC, BREAKDOWNS;YEARS MAC;MAC -0.168;0.549;BREAKDOWNS 0.810 -0.664;0.000 0.007;Cell Contents: Pearson correlation;P-ValueRegression Analysis: BREAKDOWNS;versus YEARS, MAC;The regression equation is;BREAKDOWNS = 0.462 + 1.19 YEARS - 2.68 MAC.;Predictor Coef SE Coef T;P;Constant 0.4625 0.4456 1.04 0.320;YEARS 1.1946 0.1169 10.22 0.000;MAC -2.6805 0.3470 -7.72 0.000;S = 0.649016 R-Sq = 94.2% R-Sq(adj);= 93.3%;Analysis of Variance;Source;DF SS;MS F P;Regression 2;82.679 41.339 98.14 0.000;Residual Error 12;5.055 0.421;Total 14;87.733;Predicted Values for New Observations;New Obs Fit SE;Fit 95%;CI 95% PI;1;3.755 0.367 (2.956, 4.554) (2.131, 5.379);Values of Predictors for New Observations;New Obs YEARS MAC;1 5.00 1.00;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 multiple regression t-tests on??1,??2 (use two tailed test with (a;=.10). Interpret your results.;d. Predict the total number of breakdowns for a single computer that is a;5-year-old MAC. Use both a point estimate and the appropriate interval;estimate. (Points: 31);1.(TCO E) A researcher is studying;the relationship between earnings for major electronic firms and research;and development expenditures in the previous year. A random sample of 15;major electronic firms is selected and gives the following data on R&D;(X, research, and development expenditures in the previous year in millions;of $) and EARNINGS (Y, earnings in millions of $).;R&D;EARNINGS;PREDICT;15;221;9;8.5;83;25;12;147;6.5;69;4.5;41;2;26;0.5;35;1.5;40;14;125;9;97;7.5;53;0.5;12;2.5;34;3;48;6;64;Correlations: R&D, EARNINGS;Pearson correlation of R&D;and EARNINGS = 0.919;P-Value = 0.000Regression Analysis: EARNINGS;versus R&D;The regression equation is;EARNINGS = 6.84 + 10.7 R&D;Predictor;Coef SE Coef;T P;Constant 6.843;9.781 0.70 0.497;R&D;10.671 1.266 8.43 0.000;S = 22.5948 R-Sq =;84.5% R-Sq(adj) = 83.3%;Analysis of Variance;Source;DF SS;MS F P;Regression;1 36253 36253 71.01 0.000;Residual Error;13 6637 511;Total;14 42890;Predicted Values for New;Observations;New;Obs Fit SE;Fit 95%;CI 95% PI;1 102.88 6.83 (88.13;117.63) (51.88, 153.87);2 273.61 24.51 (220.66, 326.56);(201.59, 345.62)XX;XX denotes a point that is an;extreme outlier in the predictors.;Values of Predictors for New;Observations;New Obs;R&D;1 9.0;2 25.0;a. Analyze the above output to determine the regression equation.;b. Find and interpret??1in;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 money spent on;research and development can be used to predict earnings in the following;year? 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 mean earnings for all firms that;had research and development expenditures was $9 million in the previous;year. Interpret this interval.;g. Find the 95% prediction interval for the earnings for one firm that had;research and development expenditures of $9 million. Interpret this;interval.;h. What can we say about the earnings when research and development;expenditures were $25 million? (Points: 48);1.(TCO A)Consider the following age data, which is;the result of selecting a random sample of 25 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;5;5;18;7;5 4;12 22;13;5;2;24;7;7 1;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) East;Side Bank has three loan officers, Jim, Sally, and Dave, who process all loan;applications. Each application results in an approval, rejection, or delay.;The results of the last 100 loan applications are shown below.;Jim;Sally;Dave;Total;Approved;20;16;18;54;Rejected;1;7;14;33;Delayed;5;2;6;13;Total;37;25;38;100;If you choose a loan application at random, then find the probability that;the loan application;a. was processed by Jim.;b. was approved and processed by Sally.;c. was rejected, given that the application was processed by Dave. (Points;18);Question 3. 3.(TCO B);Records of a health insurance company show that 40% of policyholders under;age 30 submitted a claim during the past year. A random sample of 75;policyholders under age 30 is selected. Assuming the records are correct;then find the probability that;a. exactly 30 submitted a claim during the past year.;b. more than 32 submitted a claim during the past year.;c. at most 29 submitted a claim during the past year. (Points: 18);Question 4. 4.(TCO B) The;end-of-month cash flow for a company can be modeled by a normal distribution;with a mean of $10,000 and a standard deviation of $7,000. Note that a;positive cash flow figure means that there is a surplus of cash, but a;negative cash flow means that we have a cash shortage.;a. Find the probability that the end-of-month cash flow will be between;$15,000 and $25,000.;b. Find the probability that the end-of-month cash flow will be at least;$5,000.;c. The treasurer is concerned about the possibility of a cash shortage and;wishes to develop strategies to manage cash flow. The treasurer wants to;establish a reserve fund that can be used in case of negative cash flow.;Suppose that the treasurer wants to be able to have a fund large enough to;cover all but 1% of the months. How much money should be in the reserve fund?;(Points: 18);Question 5. 5.(TCO C)A;survey is taken of U.S. companies that do business with firms in India. One;of the questions in the survey was: ?Approximately how many years has your;company been trading with firms in India?? A random sample of 44 responses to;this question yields the following results.;Sample Size = 44;Sample Mean = 10.46 years;Sample Standard Deviation = 7.7 years;a. Compute the 95% confidence interval for the population mean number of;years of trading with firms in India.;b. Interpret this interval.;c. How many firms should be sampled if we wish to generate a 95% confidence;interval for the mean number of years of trading with firms in India that is;accurate to within 1 year? (Points: 18);Question 6. 6.(TCO C)You;are in charge of selling advertising for radio station WQAA. The fee you can;set for airtime is directly related to the share of the listening market your;station reaches. From time to time you conduct surveys to determine WQAA?s;share of the market. This month, when you contacted 200 randomly selected;residents, 12 respondents said they listen to WQAA.;a. Compute the 99% confidence interval for the percent of the market that are;listeners of WQAA.;b. Interpret this confidence interval.;c. How many individuals should be sampled in order to be 99% confident of;being within 1% of the actual population percent of the market that are WQAA;listeners? (Points: 18);Question 7. 7.(TCO D) The;Cottrell Soap Company has produced a new dish washing liquid that it believes;is superior to competitive products on the market. The board of directors has;indicated that the product will be marketed if more than 25% of the;population of households prefer the product over its competitors. The;company?s market research department has distributed the new product to 400;randomly selected households. The results of this sampling are that 120 of;the 400 households prefer the new dish washing liquid. Does the sample data;provide evidence to conclude that the percentage of households in the;population that prefer the new dishwashing liquid is more than 25% (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 this sample data provide evidence (witha = 0.05) that the percentage of;households in the population that prefer the new dishwashing liquid is more;than 25%?;(Points: 24);Question 8. 8.(TCO D) At a;supermarket, the average number of register mistakes per day per clerk was;18. The owner of the supermarket purchased new cash registers in an effort to;decrease the number of errors. After extensive training on the new registers;the manager took a random sample of 100 clerks on randomly selected days;using the new registers and found the following results.;Sample Size = 100 clerks;Sample Mean = 17.25 mistakes per day per clerk;Sample Standard Deviation = 4.35 mistakes per day per clerk;Does the sample data provide evidence to conclude that the population mean;number of register mistakes per day per clerk was less than 18 (usinga;=.01)? 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 this sample data provide evidence (witha =.01) that the population mean;number of register mistakes per day per clerk was less than 18? (Points: 24)

Paper#61366 | Written in 18-Jul-2015

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