In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 184 with a standard deviation of 18.2982. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 17. Is there evidence that the standard deviation of test scores has increased at the α=0.01 level? Assume the population is normally distributed. Step 1 of 5 : State the null and alternative hypotheses. Round to four decimal places when necessary.

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 184 with a standard deviation of 18.2982. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 17. Is there evidence that the standard deviation of test scores has increased at the α=0.01 level? Assume the population is normally distributed. Step 1 of 5 : State the null and alternative hypotheses. Round to four decimal places when necessary.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter13: Regression And Forecasting Models

Section: Chapter Questions

Problem 32P

See similar textbooks

Similar questions

Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
A trucking company wants to predict the yearly maintenance expense (Y) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the file P13_13.xlsx. Note that each observation corresponds to a particular truck. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?
The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P13_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Is the antique collector correct in believing that the price received for the item increases with its age and with the number of bidders? Interpret the standard error of estimate and the R-square value for these data.
The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?
Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the file P13_33.xlsx. a. Create a scatterplot for these data. Comment on the observed behavior of monthly sales at this store over time. b. Estimate an appropriate regression equation to explain the variation of monthly sales over the given time period. Interpret the estimated regression coefficients. c. Analyze the estimated equations residuals. Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.
Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?
A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?
Federal Income Tax Returns. The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between$30,000and$60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was$16,642. Assume the standard deviation is σ=$2400. What is the probability that a sample of taxpayers from this in-come group who have itemized deductions will show a sample mean within$200 of the population mean for sample sizes 30?
An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold. A random survey of 15 Visa Gold cardholders resulted in a mean household income of $⁢68,420 with a standard deviation of $⁢9100. A random survey of 6 MasterCard Gold cardholders resulted in a mean household income of $⁢59,200 with a standard deviation of $⁢9200. Is there enough evidence to support the executive's claim? Let μ1 be the true mean household income for Visa Gold cardholders and μ2 be the true mean household income for MasterCard Gold cardholders. Use a significance level of α=0.05 for the test. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 4: State the null and alternative hypotheses for the test. Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places. Step 3 of 4: Determine the decision rule for rejecting the…
An engineer has designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. The valve was tested on 26 engines and the mean pressure was 4.3 pounds/square inch with a variance of 0.25. Is there evidence at the 0.01 level that the valve performs above the specifications? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses. Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.