1 POM 212 Business Statistics Homework Assignment-4 Note: The homework is due on the day of Test-4. Chapter-10 Problems: Problem-1 In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken and the following information is collected. Model A Model B Sample Size 50 55 Sample Mean 32 35 Sample Variance 9 10 a. At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. b. Is there conclusive evidence to indicate that one model gets a higher MPG than the other? Why or why not? Explain. Problem-2 Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester. University A University B Sample Size 50 40 Average Purchase $280 $250 Standard Deviation $20 $23 At 95% confidence test to determine if, on the average, students at University A spend more on textbooks then the students at University B. Problem-3 Two independent random samples of annual starting salaries for individuals with master’s and bachelor’s degrees in business were taken. Use the data shown below and provide a 95% confidence interval estimate for the difference between the salaries of the two groups. 2 Masters Degree Bachelors Degree Sample Size 14 12 Sample Mean $58,000 $55,000 Sample Standard Deviation $ 2,400 $ 2,000 Problem-4 The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let the difference "d" be: d = after - before.) Monthly Sales Salesperson After Before 1 94 90 2 82 84 3 90 84 4 76 70 5 79 80 6 85 80 Problem-5 Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results. New Machine Old Machine Sample Mean 25 23 Sample Variance 27 7.56 Sample Size 45 36 As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your answer. 3 Chapter-12 Problems: Problem-6 Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates to be as follows. Percentages Democrats 48% Republicans 38% Independent 4% Undecided 10% After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. At 95% confidence, test to see if the proportion of voters has changed. Problem-7 Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year? Use 95% confidence level. Problem-8 The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred: Season Number of Resignations Winter 10 Spring 22 Summer 19 Fall 9 Test to see if the number of resignations is uniform over the four seasons. Use 95% confidence level. 4 Problem-9 A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a domestic car. The following contingency table shows the results of the survey. CITY Type of Car Detroit Atlanta Denver Total Domestic 80 200 520 800 Foreign 120 600 480 1200 Total 200 800 1000 2000 With 95% confidence level, test to determine if the type of car purchased is independent of the city in which the purchasers live. Problem-10 Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below. Styling Engineering Fuel Economy Total Male 70 130 150 350 Female 30 20 100 150 100 150 250 500 Give your conclusion for this test with 90% confidence level. Chapter-14 Problems: Problem-11 The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Year Sales in Millions of Dollars (Y) Advertising in ($10,000) (X) 1994 15 32 1995 16 33 1996 18 35 1997 17 34 1998 16 36 1999 19 37 2000 19 39 2001 24 42 5 a. Develop a scatter diagram of sales versus advertising. b. Use the method of least squares to compute an estimated regression line between sales and advertising. Problem-12 An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 months was taken. The results of the sample are presented below. Monthly Sales (Y) Interest Rate (In Percent) (X) 22 9.2 20 7.6 10 10.4 45 5.3 a. Use the method of least squares to compute an estimated regression line. b. Obtain a measure of how well the estimated regression line fits the data. Problem-13 Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample. Cups of Coffee Sold Temperature 350 50 200 60 210 70 100 80 60 90 40 100 a. Which variable is the dependent variable? b. Compute the least squares estimated line. c. Compute the correlation coefficient between temperature and the sales of coffee. d. Predict sales of a 90 degree day. 6 Problem-14 Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below. Hours of Television Age 1 45 3 30 4 22 3 25 6 15 a. Determine which variable is the dependent variable. b. Compute the least squares estimated line. c. Compute the coefficient of determination. How would you interpret this value?