Statistics for Business & Economics, Revised (MindTap Course List)
12th Edition
ISBN: 9781285846323
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: South-Western College Pub
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Chapter 15.6, Problem 30E
a.
To determine
Find a 95% confidence interval for the mean top speed of a boat with a beam of 85 inches and engine with a 330 horsepower rating.
b.
To determine
Find a 95% prediction interval for the mean top speed for the Svfara SV609.
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In simple linear regression, at what value of the independent variable, X, will the 95% confidence interval for the average value of Y be narrowest? At what value will the 95% prediction interval for the value of Y for a single n ew observation be narrowest?
In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4.Click on the datafile logo to reference the data. Use Table 1 of Appendix B.
a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $
c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that
b1=1.4379 and Sb1=0.1397.
a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?
b. Construct a 95% confidence interval estimate of the population slope,
β1.
a. Determine the hypotheses for the test. Choose the correct answer below.
A.
H0:
β1=0
H1:
β1≠0
B.
H0:
β0≤0
H1:
β0>0
C.
H0:
β1≤0
H1:
β1>0
D.
H0:
β0≥0
H1:
β0<0
E.
H0:
β1≥0
H1:
β1<0
F.
H0:
β0=0
H1:
β0≠0
Compute the test statistic.
The test statistic is ?
(Round to two decimal places as needed.)
Determine the critical value(s).
The critical value(s) is(are) ?
(Use a comma to separate answers as needed.…
Chapter 15 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 15.2 - The estimated regression equation for a model...Ch. 15.2 - Consider the following data for a dependent...Ch. 15.2 - In a regression analysis involving 30...Ch. 15.2 - A shoe store developed the following estimated...Ch. 15.2 - The owner of Showtime Movie Theaters, Inc., would...Ch. 15.2 - The National Football League (NFL) records a...Ch. 15.2 - PC World rated four component characteristics for...Ch. 15.2 - The Cond Nast Traveler Gold List provides ratings...Ch. 15.2 - Waterskiing and wakeboarding are two popular...Ch. 15.2 - Prob. 10E
Ch. 15.3 - In exercise 1, the following estimated regression...Ch. 15.3 - Prob. 12ECh. 15.3 - In exercise 3, the following estimated regression...Ch. 15.3 - In exercise 4, the following estimated regression...Ch. 15.3 - In exercise 5, the owner of Showtime Movie...Ch. 15.3 - In exercise 6, data were given on the average...Ch. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.5 - In exercise 1, the following estimated regression...Ch. 15.5 - Refer to the data presented in exercise 2. The...Ch. 15.5 - The following estimated regression equation was...Ch. 15.5 - In exercise 4, the following estimated regression...Ch. 15.5 - Prob. 23ECh. 15.5 - The Wall Street Journal conducted a study of...Ch. 15.5 - The Cond Nast Traveler Gold List for 2012 provided...Ch. 15.5 - In exercise 10, data showing the values of several...Ch. 15.6 - In exercise 1, the following estimated regression...Ch. 15.6 - Refer to the data in exercise 2. The estimated...Ch. 15.6 - In exercise 5, the owner of Showtime Movie...Ch. 15.6 - Prob. 30ECh. 15.6 - The American Association of Individual Investors...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Management proposed the following regression model...Ch. 15.7 - Refer to the Johnson Filtration problem introduced...Ch. 15.7 - This problem is an extension of the situation...Ch. 15.7 - The Consumer Reports Restaurant Customer...Ch. 15.7 - A 10-year study conducted by the American Heart...Ch. 15.8 - Data for two variables, x and y, follow. xi 1 2 3...Ch. 15.8 - Data for two variables, x and y, follow. xi 22 24...Ch. 15.8 - Exercise 5 gave the following data on weekly gross...Ch. 15.8 - The following data show the curb weight,...Ch. 15.8 - Prob. 43ECh. 15.9 - Refer to the Simmons Stores example introduced in...Ch. 15.9 - In Table 15.12 we provided estimates of the...Ch. 15.9 - Community Bank would like to increase the number...Ch. 15.9 - Over the past few years the percentage of students...Ch. 15.9 - The Tire Rack maintains an independent consumer...Ch. 15 - The admissions officer for Clearwater College...Ch. 15 - The personnel director for Electronics Associates...Ch. 15 - A partial computer output from a regression...Ch. 15 - Recall that in exercise 49, the admissions officer...Ch. 15 - Recall that in exercise 50 the personnel director...Ch. 15 - The Tire Rack, Americas leading online distributor...Ch. 15 - The Department of Energy and the U.S....Ch. 15 - A portion of a data set containing information for...Ch. 15 - Fortune magazine publishes an annual list of the...Ch. 15 - Consumer Research, Inc., is an independent agency...Ch. 15 - Matt Kenseth won the 2012 Daytona 500, the most...Ch. 15 - Finding the Best Car Value When trying to decide...
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- Exercise #1 Open the Excel worksheet MPGDATA.XLS from Blackboard>Excel #5 Files. The data in column A of this worksheet represent the miles per gallon gasoline consumption for a random sample of 55 makes and models of passenger cars (source: Environmental Protection Agency) Use the Excel Confidence Interval Template to: Construct a 95% confidence interval for the population mean miles per gallon consumption for passenger cars. Use the Excel Hypothesis Testing Template to: Test the hypothesis that the population mean of miles per gallon gasoline consumption for passenger cars is different from 25 mpg. Use a significance level of 5%. Do we know ? for the mpg consumption? Can we use the normal distribution for the hypothesis test? State the null and alternative hypotheses. Perform the appropriate test and print the output. Look at the p-value in the output. Compare it to ?. Do we reject the null hypothesis or not? Generate the descriptive statistics (mean, standard…arrow_forwardIn exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B.Click on the datafile logo to reference the data. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$ b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $ c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).$ to $arrow_forwardIn Exercises, presume that the assumptions for regression inferences are met.Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise. x 10 10 13 13 18 19 19 23 25 28 y 66 66 108 106 161 166 177 228 235 280 a. Determine a point estimate for the mean crown-rump length of all 19-week-old fetuses.b. Find a 90% confidence interval for the mean crown-rump length of all 19-week-old fetuses.c. Find the predicted crown-rump length of a 19-week-old fetus.d. Determine a 90% prediction interval for the crown-rump length of a 19-week-old fetus.ExerciseApplying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.arrow_forward
- A U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption: Illinois Texas = 49 = 64 = 54.1lb = 60.4lb S1 = 7.0 S2 = 8.0 Develop a 95% confidence Interval Estimate for the difference between the two population means.arrow_forwardIn exercise 7, the data on y = annual sales ($1000s) for new customer accounts andx = number of years of experience for a sample of 10 salespersons provided the estimatedregression equation yˆ = 80 + 4x. For these data x = 7, o(xi − x)2 = 142, and s = 4.6098.a. Develop a 95% confidence interval for the mean annual sales for all salespersons withnine years of experience.b. The company is considering hiring Tom Smart, a salesperson with nine years of experience.Develop a 95% prediction interval of annual sales for Tom Smart.c. Discuss the differences in your answers to parts (a) and (b).arrow_forwardThe final exam score was recorded for each Harper statistics student in a sample of 30. A 95% confidence interval forarrow_forward
- 11.36 Use the data from Exercise 11.22.a. Estimate the mean time to run 10 km for athletes having a treadmill time of11 minutes.b. Place a 95% confidence interval on the mean time to run 10 km for athleteshaving a treadmill time of 11 minutes.arrow_forwardA 30 month study is conducted to determine the difference in rates of accidents per month between two departments in an assembly plant. If a sample of 12 from the first department averaged 12.3 accidents per month with a standard deviation of 3.5, and a sample of 9 from the second department averaged 7.6 accidents per month with standard deviation of 3.4, find: The t-value for a 95% confidence interval is: A. 2.09302 B. 1.724718 C. 2.08596 D. 1.729133 E. none of the precedingarrow_forwardBased on the sample data set: (0,0) ( 2,3) (3,3) (6,4) (9,8) A. Construct the 90% confidence interval for the slope B1 of the population regression line B. find the Coefficient of determination using the formula r2=B1SSxy / SSyy.arrow_forward
- An Internet retailer would like to investigate the relationship between the amount of time in minutes a purchaser spends on its Web site and the amount of money he or she spends on an order. The table to the right shows the data from a random sample of 12customers. Construct a 90% confidence interval for the regression slope. Order Size Time Order Size 17 $73 3 $60 14 $25 38 $365 26 $96 7 $126 22 $196 38 $158 1 $51 25 $76 12 $39 8 $252 Construct a 90% confidence interval for the slope. LCL= UCL= (Round to three decimal places as needed.)arrow_forwardRefer to Exercise 7.S.6. Construct a 95% confidence interval for the population mean reduction in stem length. Does the confidence interval indicate whether the effect of stress is “horticulturally important,” if “horticulturally important” is defined as a reduction in population mean stem length of at least 1 cm 2 cm 5 cmarrow_forwardThe sample observation below were randomly selected. (a) Determine the regression equation, (b) Determine the expected value of Y if X=9, (c) Determine the 0.90 confidence interval for the mean predicted when X=9, and (d) Determine the 0.90 prediction interval for an individual predicted when X=9. x 4,5,3,6,10 y 4 6 5 7 7arrow_forward
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