STAT Final exam solution correct answer key

STAT Final exam solution correct answer key

1.    (TCO A) Seventeen salespeople reported the following number of sales calls completed last month.

72 93 82 81 82 97 102 107 119
86 88 91 83 93 73 100 102 

a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of sales calls per month.

b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33)

2.      (TCO B) Consider the following data on newly hired entry-level employees in relation to how many previous positions they have held and which part of the country they were born.

If you choose one person at random, then find the probability that the person

a. had 0 previous positions. 

b. is from the West and had three or more previous positions.

c. had only one previous position, given that the person is from the Midwest. (Points : 18)

3.      (TCO B) SILCHIPS corporation is a larger manufacturer of widgets. Historically, they have maintained a defective rate of 1.8%. You purchase 100 widgets (which represents a random sample). Find the probability that

a. exactly three are defective.

b. at least five are defective.

c. fewer than four are defective. (Points : 18)

4.      (TCO B) At a local supermarket the monthly customer expenditure follows a normal distribution with a mean of $495 and a standard deviation of $121.

a. Find the probability that the monthly customer expenditure is less than $300 for a randomly selected customer. 

b. Find the probability that the monthly customer expenditure is between $300 and $600 for a randomly selected customer. 

c. The management of a supermarket wants to adopt a new promotional policy giving a free gift to every customer who spends more than a certain amount per month at this supermarket. Management plans to give free gifts to the top 8% of its customers (in terms of their expenditures). How much must a customer spend in a month to qualify for the free gift? (Points : 18)

5.      (TCO C) Parker Seal, Inc. makes O-rings for newly planned commercial space shuttles. The rings are designed to seal connections and joint fillings in the fuel system to prevent leaks. One type of ring should be 5 centimeters in diameter in order to fit properly. A sample of 49 of these type of O-rings is selected and the diameters are measured The sample results are as follows.

Sample Size = 49
Sample Mean = 5.05 centimeters. 
Sample Standard Deviation = .14 centimeters. 

a. Construct a 99% confidence interval for the average diameter of this type of O-Ring.

b. Interpret this interval. 

c. How large a sample size will need to be selected if we wish to have a 99% confidence interval for the average diameter of this type of O-Ring with a margin for error of .02 centimeters? (Points : 18)

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 residential phone numbers, 12 respondents said they listen to WQAA.

a. Compute the 99% confidence interval for the population percentage of the market who are listeners of WQAA.

b. Interpret this confidence interval.

c. How large a sample size will need to be selected if we wish to be 99% confident of being within 2% of the actual population percentage of the market who are WQAA listeners? (Points : 18)

7.      (TCO D) 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 arrive within the promised 2-day period. A randomly selected sample of 400 such parcels is found to contain 292 that were delivered on time. Does the sample data provide evidence to conclude that the percentage of on-time parcels is less than 75% (with a = .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 this sample data provide evidence (with a = .010), that the percentage of on-time parcels is more than 75%?
(Points : 24)

8.      (TCO D) A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life.

Sample Size = 36 shoes
Sample Mean = 52.3 hours
Sample Standard Deviation = 9.6 hours

Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (using a = .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 manufacturer’s claim is correct (using a = .10)? (Points : 24)

1. (TCO E) The management of JAL Airlines assumes a direct relationship between advertising expenditures and the number of passengers who choose to fly JAL. The following data is collected over the past 15 months of performance by JAL Airlines. Note that X=ADEXP (Advertising Expenditures in $1,000s), and Y=Passengers (number of passengers in 1,000s). The MINITAB printout can be found below

a. Analyze the above output to determine the regression equation.

b. Find and interpret BETA SUB 11in 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 (= .05) that advertising expenditures can be used to predict the number of passengers? 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 number of passengers when advertising expenditures were $120,000. Interpret this interval.
g. Find the 95% prediction interval for the number of passengers when advertising expenditures were $120,000. Interpret this interval.
h. What can we say about the number of passengers when advertising expenditures were $250,000? (Points : 48)

Question 1.1. (TCO E) The management of an international hotel chain is in the process of evaluating possible sites for a new hotel on a beach resort. As part of the analysis, management is interested in evaluating the relationship between the distance between a hotel and the beach, (Distance, X1 in miles), the number of golf courses on the premises (Golf, X2), and the average occupancy rate (Rate, Y as a %). A sample of 14 existing resort hotels is selected yielding the following results.

a. Analyze the above output to determine the multiple regression equation.
b. Find and interpret the multiple index of determination (R-Sq). 

c. Perform multiple regression t-tests on beta sub 1 and beta sub 2. Use two tailed test with (ae = .10). Interpret your results

d.Predict the average occupancy for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (points 31)

c. Perform the multiple regression t-tests on β˖1, β˖2 (use two tailed test with (= .10). Interpret your results.

d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)

c. Perform the multiple regression t-tests on β˖1, β˖2 (use two tailed test with (= .10). Interpret your results.
d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)

c. Perform the multiple regression t-tests on β˖1, β˖2 (use two tailed test with (= .10). Interpret your results.
d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)

c. Perform the multiple regression t-tests on β˖1, β˖2 (use two tailed test with (= .10). Interpret your results.
d. Predict the average occupancy rate for a single hotel that is .5 miles from the beach and has two golf courses on the premises. Use both a point estimate and the appropriate interval estimate. (Points : 31)

1. (TCO A) Seventeen salespeople reported the following number of sales calls completed last month. 72 93 82 81 82 97 102 107 119 86 88 91 83 93 73 100 102 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of sales calls per month. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) 2. (TCO B) Consider the following data on newly hired entry-level employees in relation to how many previous positions they have held and which part of the country they were born. 0 1 2 3 or more Total East 3 5 2 1 11 Midwest 7 9 2 0 18 West 1 7 8 5 21 Total 11 21 12 6 50 If you choose one person at random, then find the probability that the person a. had 0 previous positions. b. is from the West and had three or more previous positions. c. had only one previous position, given that the person is from the Midwest. (Points : 18) 3. (TCO B) SILCHIPS corporation is a larger manufacturer of widgets. Historically, they have maintained a defective rate of 1.8%. You purchase 100 widgets (which represents a random sample). Find the probability that a. exactly three are defective. b. at least five are defective. c. fewer than four are defective. (Points : 18) 4. (TCO B) At a local supermarket the monthly customer expenditure follows a normal distribution with a mean of $495 and a standard deviation of $121. a. Find the probability that the monthly customer expenditure is less than $300 for a randomly selected customer. b. Find the probability that the monthly customer expenditure is between $300 and $600 for a randomly selected customer. c. The management of a supermarket wants to adopt a new promotional policy giving a free gift to every customer who spends more than a certain amount per month at this supermarket. Management plans to give free gifts to the top 8% of its customers (in terms of their expenditures). How much must a customer spend in a month to qualify for the free gift? (Points : 18) 5. (TCO C) Parker Seal, Inc. makes O-rings for newly planned commercial space shuttles. The rings are designed to seal connections and joint fillings in the fuel system to prevent leaks. One type of ring should be 5 centimeters in diameter in order to fit properly. A sample of 49 of these type of O-rings is selected and the diameters are measured The sample results are as follows. Sample Size = 49 Sample Mean = 5.05 centimeters. Sample Standard Deviation = .14 centimeters. a. Construct a 99% confidence interval for the average diameter of this type of O-Ring. b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval for the average diameter of this type of O-Ring with a margin for error of .02 centimeters? (Points : 18) 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 residential phone numbers, 12 respondents said they listen to WQAA. a. Compute the 99% confidence interval for the population percentage of the market who are listeners of WQAA. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to be 99% confident of being within 2% of the actual population percentage of the market who are WQAA listeners? (Points : 18) 7. (TCO D) 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 arrive within the promised 2-day period. A randomly selected sample of 400 such parcels is found to contain 292 that were delivered on time. Does the sample data provide evidence to conclude that the percentage of on-time parcels is less than 75% (with a = .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 this sample data provide evidence (with a = .010), that the percentage of on-time parcels is more than 75%? (Points : 24) 8. (TCO D) A manufacturer of athletic footwear claims that the mean life of his product will exceed 50 hours. A random sample of 36 shoes leads to the following results in terms of useful life. Sample Size = 36 shoes Sample Mean = 52.3 hours Sample Standard Deviation = 9.6 hours Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (using a = .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 manufacturer’s claim is correct (using a = .10)? (Points : 24)