Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Chapter 1.4, Problem 99E
Dental Hygiene: Which Toothbrush? In an experiment reported by J. Singer and D. Andrade in the article “Regression Models for the Analysis of Pretest/Posttest Data” (Biometrics, Vol. 53, pp. 729–735), the effect of using either a conventional or experimental (hugger) toothbrush was investigated. Twelve female and 12 male preschoolers were selected. Within each gender group, six were randomly assigned to the conventional toothbrush and the remaining six to the experimental toothbrush. After each subject brushed with the assigned toothbrush, a dental plaque index was measured. The higher the dental plaque index, the greater was the amount of plaque on an individual’s teeth.
- a. Is the statistical design described here a completely randomized design or a randomized block design? Explain your answer.
- b. If the statistical design is a randomized block design, what are the blocks?
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Dental Hygiene: Which Toothbrush? In an experiment reported by J. Singer and D. Andrade in the article “Regression Models for the Analysis of Pretest/Posttest Data” (Biometrics, Vol. 53, pp. 729–735), the effect of using either a conventional or experimental (hugger) toothbrush was investigated. Twelve female and 12 male preschoolers were selected. Within each gender group, six were randomly assigned to the conventional toothbrush and the remaining six to the experimental toothbrush. After each subject brushed with the assigned toothbrush, a dental plaque index was measured. The higher the dental plaque index, the greater was the amount of plaque on an individual’s teeth.
a. Is the statistical design described here a completely randomized design or a randomized block design? Explain your answer.b. If the statistical design is a randomized block design, what are the blocks?
Consider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to
test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+
B2 != 0 (!= means "not equal to"). The data set consists of 100 observations.
(a) Suppose we use an F-statistic to conduct the test. What are the degrees of
freedom associated with this test statistic?
(b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote
the actual F-statistic by F_act. Suppose someone says that you should reject the null
at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this
approach.
(c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield
very different p-values. Do you think this result is correct? Briefly explain your
reasoning.
Protein Content of Wheat. In their text, Methods of Correlation and Regression Analysis (New York: Wiley, 1959), M. Ezekiel and K. Fox present, for 20 batches of wheat, data on protein content and proportion of (hard, dark) vitreous kernels, as seen in the following table.
Protein content is found by expensive chemical analysis,whereas proportion of vitreous kernels is found by visual inspection. To provide an inexpensive way for predicting protein content, we want to obtain an appropriate regression equation for relating protein content to proportion of vitreous kernels. Use Procedure B.1 on page B-13 to determine a suitable regression equation.
Chapter 1 Solutions
Introductory Statistics (10th Edition)
Ch. 1.1 - Define the following terms: a. Population b....Ch. 1.1 - What are the two major types of statistics?...Ch. 1.1 - Identify some methods used in descriptive...Ch. 1.1 - Explain two ways in which descriptive statistics...Ch. 1.1 - Define the following terms: a. Observational study...Ch. 1.1 - Fill in the following blank: Observational studies...Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...
Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...Ch. 1.1 - In Exercises 1.71.12, classify each of the studies...Ch. 1.1 - Thoughts on Evolution. In an article titled Who...Ch. 1.1 - Big-Banks Break-up. A nationwide survey of 1000...Ch. 1.1 - Genocide. The document American Attitudes about...Ch. 1.1 - Vasectomies and Prostate Cancer. Refer to the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - In Exercises 1.171.22, state whether the...Ch. 1.1 - Ballistic Fingerprinting. In an on-line press...Ch. 1.1 - Causes of Death. The National Center for Health...Ch. 1.1 - Medical Testing on Animals. In its Summer 2013...Ch. 1.1 - Lobbying Congress. In the special report, Bitter...Ch. 1.2 - Explain why a census is often not the best way to...Ch. 1.2 - Identify two statistical methods other than a...Ch. 1.2 - In sampling, explain why obtaining a...Ch. 1.2 - Provide a scenario of your own in which a sample...Ch. 1.2 - Regarding probability sampling: a. What is it? b....Ch. 1.2 - Regarding simple random sampling: a. What is...Ch. 1.2 - The inferential procedures discussed in this book...Ch. 1.2 - Identify two methods for obtaining a simple random...Ch. 1.2 - What is the acronym used for simple random...Ch. 1.2 - The members of a population are numbered 15. a....Ch. 1.2 - The members of a population are numbered 14. a....Ch. 1.2 - The members of a population are numbered 190. a....Ch. 1.2 - The members of a population are numbered 150. a....Ch. 1.2 - Memorial Day Poll. In the year 2000, an on-line...Ch. 1.2 - Estimating Median Income. Explain why a sample of...Ch. 1.2 - Oklahoma State Officials. The five top Oklahoma...Ch. 1.2 - Oklahoma State Officials. The five top Oklahoma...Ch. 1.2 - Best-Selling Albums. The Recording Industry...Ch. 1.2 - Best-Selling Albums. Refer to Exercise 1.44. a....Ch. 1.2 - Best-Selling Albums. Refer to Exercise 1.44. a....Ch. 1.2 - Social Networking Websites. From Wikipedia.com, we...Ch. 1.2 - Keno. In the game of keno, 20 balls are selected...Ch. 1.2 - The International 500. Each year, Fortune Magazine...Ch. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Undercoverage. Oftentimes, an accurate and...Ch. 1.2 - Nonresponse. When responses are not obtained from...Ch. 1.2 - Response bias. When the behavior of the...Ch. 1.3 - In each of Exercises 1.551.58, fill in the...Ch. 1.3 - In each of Exercises 1.551.58, fill in the...Ch. 1.3 - In each of Exercises 1.551.58, fill in the...Ch. 1.3 - In each of Exercises 1.551.58, fill in the...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - The members of a population have been numbered...Ch. 1.3 - Ghost of Speciation Past. In the article, Ghost of...Ch. 1.3 - Number of Farms. The National Agricultural...Ch. 1.3 - John F. Kennedy. In one of his books, Ted...Ch. 1.3 - Litigation Surveys. In the article,...Ch. 1.3 - Immunization of Schoolchildren. In the article,...Ch. 1.3 - University Parking Facilities. During one year, a...Ch. 1.3 - The International 500. In Exercise 1.49 on page...Ch. 1.3 - Keno. In the game of keno, 20 balls are selected...Ch. 1.3 - Sampling Dorm Residents. Students in the...Ch. 1.3 - Best High Schools. In an issue of Newsweek (Vol....Ch. 1.3 - U.S. House of Representatives. There are 435...Ch. 1.3 - Prob. 76ECh. 1.3 - Prob. 77ECh. 1.3 - In simple random sampling, all samples of a given...Ch. 1.3 - In simple random sampling, it is also true that...Ch. 1.3 - In simple random sampling, it is also true that...Ch. 1.4 - In a designed experiment, a. what are the...Ch. 1.4 - State and explain the significance of the three...Ch. 1.4 - Prob. 83ECh. 1.4 - In this section, we discussed two types of...Ch. 1.4 - In a designed experiment, there is one factor with...Ch. 1.4 - In a designed experiment, there is one factor with...Ch. 1.4 - Prob. 87ECh. 1.4 - In a designed experiment, there are two factors,...Ch. 1.4 - In a designed experiment, there are two factors....Ch. 1.4 - Adverse Effects of Prozac. Prozac (fluoxetine...Ch. 1.4 - Treating Heart Failure. In the journal article...Ch. 1.4 - In Exercises 1.921.97, we present descriptions of...Ch. 1.4 - Prob. 93ECh. 1.4 - In Exercises 1.921.97, we present descriptions of...Ch. 1.4 - Prob. 95ECh. 1.4 - In Exercises 1.921.97, we present descriptions of...Ch. 1.4 - In Exercises 1.921.97, we present descriptions of...Ch. 1.4 - Prob. 98ECh. 1.4 - Dental Hygiene: Which Toothbrush? In an experiment...Ch. 1.4 - The Salk Vaccine. In Exercise 1.17 on page 8, we...Ch. 1.4 - In sampling from a population, state which type of...Ch. 1 - Almost any inferential study involves aspects of...Ch. 1 - Regarding observational studies and designed...Ch. 1 - Before planning and conducting a study to obtain...Ch. 1 - Explain the meaning of a. a representative sample....Ch. 1 - Which of the following sampling procedures involve...Ch. 1 - Describe each of the following sampling methods...Ch. 1 - Identify and explain the significance of the three...Ch. 1 - Baseball Scores. From ESPN MLB Scoreboard, we...Ch. 1 - Working Lottery Winners. In a national poll taken...Ch. 1 - British Backpacker Tourists. Research by G. Visser...Ch. 1 - Peanut Allergies. In the article Food Allergy...Ch. 1 - Persistent Poverty and IQ. An article appearing in...Ch. 1 - Wasp Hierarchical Status. In an issue of Discover...Ch. 1 - Incomes of College Students Parents. A researcher...Ch. 1 - On-Time Airlines. From the FlightStats On-time...Ch. 1 - Top North American Athletes. As part of ESPNs...Ch. 1 - QuickVote. TalkBack Live, a production of CNN,...Ch. 1 - Leisure Activities and Dementia. An article...Ch. 1 - Hepatitis B and Pancreatic Cancer. The article...Ch. 1 - Top North American Athletes. Refer to Problem 17....Ch. 1 - Water Quality. In the article Randomized...Ch. 1 - Prob. 23RPCh. 1 - Plant Density and Tomato Yield. In Effects of...Ch. 1 - Child-Proof Bottles. Designing medication...Ch. 1 - Prob. 26RPCh. 1 - Comparing Gas Mileages. An experiment is to be...Ch. 1 - The file named Focus.txt in the Focus Database...Ch. 1 - At the beginning of this chapter, we discussed the...
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- Protein Content of Wheat. In their text, Methods of Correlation and Regression Analysis (New York: Wiley, 1959), M. Ezekiel and K. Fox present, for 20 batches of wheat, data on protein content and proportion of (hard, dark) vitreous kernels, as seen in the following table. Protein content is found by expensive chemical analysis,whereas proportion of vitreous kernels is found by visual inspection. To provide an inexpensive way for predicting protein content, we want to obtain an appropriate regression equation for relating protein content to proportion of vitreous kernels.arrow_forwardMultiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. Which of the independent variables is the most significant predictor of the cash price of wheat? a. Intercept b. Economic Growth c. Population Growth d. Meat Consumptionarrow_forwardMultiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation Based on a significance level of 5%, which of the following independent variables significantly predict the cash price of wheat? a. Economic Growth b. Population Growth c. Meat Consumption d. All the independent variables significantly predict the cash price of wheat.arrow_forward
- Multiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. The actual cash price of wheat under investigation in 1963 was $2.13. Based on the comparison of the correct predicted cash price calculated in the previous question and the actual cash price, what does the evidence suggest about Cargill, Inc.? a. Because the predicted price is relatively close to the actual price (within one cent), Cargill, Inc. probably did not artificially manipulate the price of wheat.…arrow_forwardMultiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. In 1963, during the period in question, economic growth was 3.8; population growth was 1.40; and meat consumption was 152.95. Based on these values, what would be the predicted cash price of wheat at this time in 1963?arrow_forwardMultiple regression is sometimes used in litigation. In the case of Cargill, Inc. v. Hardin (1971), the prosecution charged that the cash price of wheat was manipulated in violation of the Commodity Exchange Act. In a statistical study conducted for this case, a multiple regression model was constructed to predict the cash price of wheat using three supply-and-demand explanatory variables: economic growth, population growth, and meat consumption. Data for 24 years were used to construct the regression equation, and a prediction for the suspect period was computed from this equation. The following output represents the regression analysis. . Before the judge and jury consider the results of the regression model, they must ensure that the model is valid. What is the proper hypothesis test for this model, and what is the proper conclusion?arrow_forward
- The average asking rent for 10 markets, and the corresponding monthly mortgage on the median priced home (including taxes and insurance) for 10 cities are given in Rent ($) Mortgage ($) City 1 840 539 City 2 1062 1002 City 3 823 626 City 4 779 711 City 5 796 655 City 6 1071 977 City 7 953 776 City 8 851 695 City 9 762 651 City 10 723 654 What is the quadratic regression model to predict the monthly mortgage on the median priced home, using average asking rent? Fill in the coefficient for the Quadratic independent variable (keep 3 decimal points).arrow_forwarda) Calculate the least square regression line for X on Y of the given data?b) Calculate the coefficient of correlation of the given date? Interpret the value of the coefficient?arrow_forward9. The F-test used in testing the significance of a regression model is A. Upper tailed test B. Two tailed test . C. Lower tailed test D. Nonearrow_forward
- Computer output from a least-squares regression analysis based on a sample of size 17 is shown in the table. Term COEFCOEF SE CoefSE Coef TT Constant 7.43 0.59 12.59 xx 5.65 1.14 6.45 Assuming all conditions for inference are met, which of the following defines a 95 percent confidence interval for the slope of the least-squares regression line?arrow_forwardA manufacturer of car batteries claims that the mean lifetime of their battery is 67 months. Thinking that this claim is inflated, graduate students buy a random sample of 72 car batteries from this manufacturer. How should they proceed? a) Perform a hypothesis test of H0:μ=67 versus Ha:μ>67 b) Perform a hypothesis test of H0:μ=67 versus Ha:μ<67 c) Use Simple linear regressionarrow_forwardLike father, like son: In 1906 , the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 7 pairs, with height measured in inches, simulated from the distribution specified by Pearson. Father'sheight Son'sheight 65.4 66.0 73.6 74.9 68.3 68.3 66.7 68.8 69.1 71.8 70.7 71.0 69.3 71.4 Compute the least-squares regression line for predicting son's height ( y) from father's height (x). Round the slope and y-intercept values to at least four decimal places.arrow_forward
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