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STATS Final Examination Questions Set

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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.?;P(X=9) = 15C9*0.6^9*0.4^6 = 0.2066;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)P;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);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)

 

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