ES9 Additional Exercises
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Chapter 111. A nationwide survey of consumers in 1998 was conducted to determine the level of uncertainty surrounding the Y2K problem. CIO Communications, Inc. asked heads of households, “What are you planning to do with your money if the Y2K problem isn’t solved by mid-1999?” The results are shown in the table below:
Source: Newsweek, “Don’t Bank on It”, August 24, 1998, p. 9. Suppose a local follow-up survey is conducted using 300 respondents from your city who answer exactly the same question. Results from the follow-up study are tabulated below:
Does the distribution of responses differ from the distribution obtained from the nationwide survey? Test at the 0.05 level of significance. a. Solve using the p-value approach. b. Solve using the classical approach. 2. An article titled "Human Papillomavirus Infection and Its Relationship to Recent and Distant Sexual Partners" (Obstetrics & Gynecology, November 1994) gave the following results concerning age and the percent who were HPV-positive among the 290 participants in the study. Age N HPV-Positive (%) 20 27 40.7 21-25 81 37.0 26-30 108 31.5 31-35 74 24.3 Complete the test of the hypothesis that the same proportion of each age group is HPV-positive for the population this sample represents. Use 05. a. Solve using the p-value approach. b. Solve using the classical approach.
1. An article titled “A Contrast in Images: Nursing and Nonnursing College Students” (Nursing Education, March 1994) described a seven-point Likert scale questionnaire to compare nursing students, business majors, engineering majors, human service majors, and social science majors with respect to several attitudes towards nursing. The nonnursing students found nursing a significantly less dangerous profession than did the nursing students. A sample of five students from each of the five majors were asked to respond to the danger associated with the nursing profession. The scores for each of the 25 students are given below. Nursing Business Engineering Human Services Social Science 6 4 5 4 3 5 4 4 4 3 5 3 4 5 2 7 3 6 4 4 4 2 2 6 2 Complete an ANOVA table for the above data. Test the null hypothesis that the mean score is the same for each of the five groups. Use the 0.01 level of significance. a. Solve using the p-value approach. b. Solve using the classical approach. 2. “All tillage tools are not created equal,” according to Larry Reichenberger as he reported in Successful Farming, February 1979. The table below presents the yield per plot obtained in an experiment designed to compare six different methods of tilling the ground.
Replicates: 118.3 115.8 124.1 109.2 118.1 118.3 125.6 122.5 118.5 114.0 117.5 113.7 123.8 118.9 113.3 122.5 121.4 113.7 Construct a dotplot showing the six samples separately and side by side. Using one-way ANOVA, test the claim that “all tillage tools are not created equal.” Use = 0.05. b. State the null and alternative hypotheses and describe the meaning of each. c. Complete using the p-value approach. d. Complete using the classical approach. 3. Stock funds are a popular form of mutual fund investment, and several types of funds are available to investors. Like other forms of investment, stock funds are thought to vary in the degree of risk associated with them. The table below shows five types of stock funds: Aggressive Growth, Small Company, Growth, Growth and Income, and International. Ten funds were selected for each type, based upon the highest returns they provided to their investors over the past five years. The numbers in the table are the measure of risk (volatility) exhibited by the stock fund.
Source: Fortune, “The Best Mutual Funds”, August 17, 1998, p. 88. Does this sample indicate that risk differs from one category of stock fund to the next? Using one-way ANOVA, test at the 0.01 level of significance to determine if there is a difference in the mean risk levels measured for the five types of stock funds. a. Solve using the p-value approach. b. Solve using the classical approach. 4. The May 16, 1994 issue of Fortune magazine gave the percent change in home prices during 1993 for the top five markets as follows: Denver 12.7%, Salt Lake City-Ogden 9.7%, Miami-Hialeah 8.3%, Nashville 7.0%, and Portland 7.0%. The following data represent the percent change in home prices for randomly selected homes in St. Louis, Kansas City, and Oklahoma City. St. Louis Kansas City Oklahoma City 3.0 4.5 1.0 2.5 2.5 -2.5 -1.5 7.0 -3.5 4.0 9.0 2.0 -1.0 1.5 4.6 5.5 2.0 0.5 Complete an ANOVA table for the above data. Test the null hypothesis that the mean percent change is equal for the three cities. Use a 0.01 level of significance. a. Solve using the p-value approach. b. Solve using the classical approach.
1. The 1994 World Almanac and Book of Facts gives the Nielsen TV ratings for the favorite syndicated programs for 1992-1993. The following table gives these ratings for women, men, teenagers, and children. Women Men Teenagers Children 11.8 8.0 3.3 3.4 9.9 6.9 3.0 2.3 7.1 9.2 6.4 5.1 6.5 8.2 5.8 4.8 8.4 3.4 2.7 1.7 6.4 5.0 2.1 1.9 4.9 4.7 4.6 5.8 4.1 4.5 6.8 4.7 6.3 4.5 1.7 1.6 5.1 4.2 2.3 1.8 5.6 4.0 1.8 1.6 4.8 4.7 3.1 2.9 4.4 4.1 3.4 3.8 4.2 4.2 4.0 3.4 4.1 3.2 4.6 7.4 4.4 3.1 5.8 4.3 3.7 4.9 3.4 3.2 4.3 2.7 3.4 2.2 3.3 4.6 2.1 2.2 2.5 4.0 5.2 5.6 Calculate r and use it to determine a 95% confidence interval on for each of the following cases. a. Women and Men b. Women and Teenagers c. Women and Children d. Men and Teenagers e. Men and Children f. Teenagers and Children g. What can be concluded from the above answers? Be specific. 2. A paper titled “Blue Grama Response to Zinc Source and Rates” by E. M. White (Journal of Range Management, January 1991) described five different experiments involving herbage yield and zinc application. Some of the data in experiment number two were as follows: Grams of Zinc per kg Soil 0.0 0.1 0.2 0.4 0.8 Grams of Herbage 3.2 2.8 2.6 2.0 0.1 The paper quotes the correlation coefficient as equal to -0.99 and the line of best fit as  = -3.825x + 3.29, where x = grams of zinc and y = grams of herbage.
a. Verify the value for r. b. Verify the equation of the line of best fit. 3. A stockbroker once claimed that an investor should always refrain from buying expensive stocks. Why? “Lower- priced stocks will jump faster, percentage-wise, in a bull market than higher-priced stocks because they have more room to climb in the first place,” he touted. “It’s simple mathematics.” But wait a minute. Isn’t that a double-edged sword? Won’t lower-priced stocks fall faster, percentage-wise, especially when the bear takes over? Let the data speak for itself. The following table of 30 stocks was assembled from The Wall Street Journal’s list of the biggest price percentage gainers and losers following trading on August 17, 1998. Closing prices have been converted from fractions to decimals:
Source: The Wall Street Journal, Vol. CII, No. 35, August 19. 1998. a. Draw two scatter diagrams of the data, one for losers and the other for gainers. In each case, use percent change in price as the dependent variable (y) and closing price as the independent variable (x). b. Find the two equations for the lines of c. Are the values of the coefficients for the slopes of the two regression lines not equal to zero? Use = 0.05 and draw your conclusions in each case. 4. Politicians have often debated over how to improve the quality of education in the United States. Some argue that teachers’ salaries should be increased, whereas others claim that more teachers should be hired to reduce the number of pupils per teacher. The percentage of students graduating (graduation rate) from public high school is frequently used as an overall measure of the quality of education in a given area. The following table summarizes all three variables of interest measured in 1995 for each state and the District of Columbia.
Source: National Center for Education Statistics, U.S. Dept. of Education, National Education Association a. Draw two scatter diagrams of the data using graduation rate as the dependent variable (y) together with (1) pupils per teacher as the independent variable (x) and (2) average teacher pay as the independent variable (x). b. Find the two equations for the lines of c. Are the values of the coefficients for the slopes of the (1) pupils per teacher regression line less than zero and (2) teacher pay line greater than zero? Use = 0.05 and draw your conclusions in each case. 5. There are at least two ways that special television programs could be rated, and both are of interest to advertisers trying to promote their products--the estimated size of the audience and a rating based on the percentage of TV-owning households that tuned into the program. The table below lists the top 20 most popular televised programs as compiled by Nielsen Media Research that includes broadcasts through January, 1997:
Source: World Almanac Book of Facts 1998, “All-Time Top Televison Programs”. a. Draw a scatter diagram of these data with audience size as the dependent variable y, and rating percentage as the predictor variable, x. b. Calculate the regression equation and draw the regression line on the scatter diagram. c. If the next Super Bowl obtains a 50.0% rating, what would you estimate the audience size to be? Make your estimate based on the equation, and then draw a line on the scatter diagram to illustrate it. d. Construct a 95% prediction interval for the estimate you obtained in (c). 6. The table below contains the Metropolitan Life Insurance Company weight chart for women using three different “frame” categories and using height as the input variable, x.
a. Construct a scatter diagram showing the intervals for small-frame women. b. Construct a scatter diagram showing the intervals for medium-frame women. c. Construct a scatter diagram showing the intervals for large-frame women. d. Does it appear that the variables, “height” and “weight” have a linear relationship? Why do the scatter diagrams seem to suggest such a strong relationship? e. One inch of height adds how many pounds to the ideal weight? How is the number of pounds per inch related to the line of best fit? Directory: resource uploads -> downloads downloads -> Chapter 19 Chapter Outline downloads -> Chapter 1 Practice Quiz Introducing the Economic Way of Thinking downloads -> Bltc-8e Case Problem with Sample Answer Chapter 30: Partnerships 20. 5 Case Problem with Sample Answer downloads -> Cross-7e: Case Problem with Sample Answer downloads -> Atmospheric circulation downloads -> September 3, 2007 downloads -> August 30 2009 Website Update downloads -> Chapter 3 exercises downloads -> Review Sheet: Chapt. 1: The Moral Point of View Moral concerns are unavoidable in life. Ethics downloads -> Chapter 17 Chapter Outline Download 0.58 Mb. Share with your friends:
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