Studies show that the concentration of PCBs is much higher in malignant breast tissue than in normal breast tissue. If a study of 50 women with breast cancer reveals an average PCB concentration of 22.8 × 10−4 gram, with a standard deviation of 4.8 × 10−4 gram, is the mean concentration of PCBs less than 24 × 10−4 gram?
> How large a sample is required in Exercise 10.24 if the power of the test is to be 0.95 when the true average height differs from 162.5 by 3.1 centimeters? Use α = 0.02. Exercise 10.24: The average height of females in the freshman class of a certain co
> If the distribution of life spans in Exercise 10.19 is approximately normal, how large a sample is required in order that the probability of committing a type II error be 0.1 when the true mean is 35.9 months? Assume that σ = 5.8 months. Exercise 10.19:
> How large a sample is required in Exercise 10.20 if the power of the test is to be 0.90 when the true mean is 5.20? Assume that σ = 0.24. Exercise 10.20: A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standar
> In Review Exercise 9.91 on page 313, use the t-distribution to test the hypothesis that the diet reduces a woman’s weight by 4.5 kilograms on average against the alternative hypothesis that the mean difference in weight is less than 4.5
> A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same car
> In a study conducted by the Department of Human Nutrition and Foods at Virginia Tech, the following data were recorded on sorbic acid residuals, in parts per million, in ham immediately after dipping in a sorbate solution and after 60 days of storage:
> With reference to Exercise 11.1 on page 398, (a) evaluate s2; (b) test the hypothesis that β1 = 0 against the alternative that β1 = 0 at the 0.05 level of significance and interpret the resulting decision. Exercise 11.1: A stud
> According to published reports, practice under fatigued conditions distorts mechanisms that govern performance. An experiment was conducted using 15 college males, who were trained to make a continuous horizontal right-to-left arm movement from a microsw
> Five samples of a ferrous-type substance were used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two subsamples and the two types of analysi
> A study was conducted by the Department of Zoology at Virginia Tech to determine if there is a significant difference in the density of organisms at two different stations located on Cedar Run, a secondary stream in the Roanoke River drainage basin. Sewa
> In a study conducted at Virginia Tech, the plasma ascorbic acid levels of pregnant women were compared for smokers versus nonsmokers. Thirty-two women in the last three months of pregnancy, free of major health disorders and ranging in age from 15 to 32
> A fabric manufacturer believes that the proportion of orders for raw material arriving late is p = 0.6. If a random sample of 10 orders shows that 3 or fewer arrived late, the hypothesis that p = 0.6 should be rejected in favor of the alternative p < 0.6
> The following data represent the running times of films produced by two motion-picture companies: Test the hypothesis that the average running time of films produced by company 2 exceeds the average running time of films produced by company 1 by 10 min
> A UCLA researcher claims that the average life span of mice can be extended by as much as 8 months when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diets are enriched to normal levels by vitam
> In Exercise 9.42 on page 295, test the hypothesis that the fuel economy of Volkswagen mini-trucks, on average, exceeds that of similarly equipped Toyota mini-trucks by 4 kilometers per liter. Use a 0.10 level of significance. Exercise 9.42: An experimen
> Engineers at a large automobile manufacturing company are trying to decide whether to purchase brand A or brand B tires for the company’s new models. To help them arrive at a decision, an experiment is conducted using 12 of each brand.
> To find out whether a new serum will arrest leukemia, 9 mice, all with an advanced stage of the disease, are selected. Five mice receive the treatment and 4 do not. Survival times, in years, from the time the experiment commenced are as follows: At the
> A professor in the School of Business in a university polled a dozen colleagues about the number of professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (y) during the same period. Th
> A study was made to determine if the subject matter in a physics course is better understood when a lab constitutes part of the course. Students were randomly selected to participate in either a 3-semesterhour course without labs or a 4-semester-hour cou
> A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times, with an average velocity of 7.5
> Amstat News (December 2004) lists median salaries for associate professors of statistics at research institutions and at liberal arts and other institutions in the United States. Assume that a sample of 200 associate professors from research institutions
> A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms. To test this claim, 50 pieces of each type of thread were tested under similar conditions. Type A thread had an
> A random sample of size n1 = 25, taken from a normal population with a standard deviation σ1 = 5.2, has a mean ¯x1 = 81. A second random sample of size n2 = 36, taken from a different normal population with a standard deviation σ2 = 3.4, has a mean ¯x2 =
> A large manufacturing firm is being charged with discrimination in its hiring practices. (a) What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? (b) What hypothesis is being tested if a jury commits a type II erro
> Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete this
> According to Chemical Engineering, an important property of fiber is its water absorbency. The average percent absorbency of 25 randomly selected pieces of cotton fiber was found to be 20 with a standard deviation of 1.5. A random sample of 25 pieces of
> A study at the University of Colorado at Boulder shows that running increases the percent resting metabolic rate (RMR) in older women. The average RMR of 30 elderly women runners was 34.0% higher than the average RMR of 30 sedentary elderly women, and th
> According to a dietary study, high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready-to-eat cereals. If a ran
> A study of the amount of rainfall and the quantity of air pollution removed produced the following data: (a) Find the equation of the regression line to predict the particulate removed from the amount of daily rainfall. (b) Estimate the amount of parti
> It is claimed that automobiles are driven on average more than 20,000 kilometers per year. To test this claim, 100 randomly selected automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random
> The average height of females in the freshman class of a certain college has historically been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sampl
> Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance
> In the American Heart Association journal Hypertension, researchers report that individuals who practice Transcendental Meditation (TM) lower their blood pressure significantly. If a random sample of 225 male TM practitioners meditate for 8.5 hours per w
> An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Test the hypothesis that μ = 800 hours against the alternative, μ = 800 hours, if a
> A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standard deviation of 0.24 ounce. Test the hypothesis that μ = 5.5 ounces against the alternative hypothesis, μ < 5.5 ounces, at the 0.05 level of significance.
> A sociologist is concerned about the effectiveness of a training course designed to get more drivers to use seat belts in automobiles. (a) What hypothesis is she testing if she commits a type I error by erroneously concluding that the training course is
> In a research report, Richard H. Weindruch of the UCLA Medical School claims that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any re
> If we plot the probabilities of failing to reject H0 corresponding to various alternatives for μ (including the value specified by H0) and connect all the points by a smooth curve, we obtain the operating characteristic curve of the test criterion, or si
> A new curing process developed for a certain type of cement results in a mean compressive strength of 5000 kilograms per square centimeter with a standard deviation of 120 kilograms. To test the hypothesis that μ = 5000 against the alternative that μ < 5
> A study was done to study the effect of ambient temperature x on the electric power consumed by a chemical plant y. Other factors were held constant, and the data were collected from an experimental pilot plant. (a) Plot the data. (b) Estimate the slop
> Repeat Exercise 10.15 for samples of size n = 25. Use the same critical region. Exercise 10.15: A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 200 milliliters
> A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 200 milliliters and a standard deviation of 15 milliliters. The machine is checked periodically by taking a samp
> A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms,
> Suppose, in Exercise 10.12, we conclude that 60% of the voters favor the gasoline sales tax if more than 214 but fewer than 266 voters in our sample favor it. Show that this new critical region results in a smaller value for α at the expense of increasin
> A random sample of 400 voters in a certain city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for street repairs. If more than 220 but fewer than 260 favor the sales tax, we shall conclude that 60% of the vo
> Repeat Exercise 10.8 but assume that 70 patients are given the mussel extract and the critical region is defined to be x < 24, where x is the number of osteoarthritic patients who receive relief. Exercise 10.8: In Relief from Arthritis published by Thor
> Repeat Exercise 10.9 but assume that 100 spots are treated and the critical region is defined to be x > 82, where x is the number of spots removed. Exercise 10.9: A dry cleaning establishment claims that a new spot remover will remove more than 70% of t
> Suppose that an allergist wishes to test the hypothesis that at least 30% of the public is allergic to some cheese products. Explain how the allergist could commit (a) a type I error; (b) a type II error.
> z-Value for Testing p1−p2 = d0: To test the null hypothesis H0 that p1−p2 = d0, where d0 ≠0, we base our decision on which is a value of a random variable whose distribution approximates the standa
> The thrust of an engine (y) is a function of exhaust temperature (x) in â—¦ F when other important variables are held constant. Consider the following data. (a) Plot the data. (b) Fit a simple linear regression to the data and plot th
> The following data show the numbers of defects in 100,000 lines of code in a particular type of software program developed in the United States and Japan. Is there enough evidence to claim that there is a significant difference between the programs devel
> In a study conducted by the Water Resources Center and analyzed by the Statistics Consulting Center at Virginia Tech, two different wastewater treatment plants are compared. Plant A is located where the median household income is below $22,000 a year, an
> In a study conducted by the Department of Mechanical Engineering and analyzed by the Statistics Consulting Center at Virginia Tech, steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied
> A study was conducted at the Department of Health and Physical Education at Virginia Tech to determine if 8 weeks of training truly reduces the cholesterol levels of the participants. A treatment group consisting of 15 people was given lectures twice a w
> A study was conducted at the Virginia-Maryland Regional College of Veterinary Medicine Equine Center to determine if the performance of a certain type of surgery on young horses had any effect on certain kinds of blood cell types in the animal. Fluid sam
> A study was made to determine whether there is a difference between the proportions of parents in the states of Maryland (MD), Virginia (VA), Georgia (GA), and Alabama (AL) who favor placing Bibles in the elementary schools. The responses of 100 parents
> If one can containing 500 nuts is selected at random from each of three different distributors of mixed nuts and there are, respectively, 345, 313, and 359 peanuts in each of the cans, can we conclude at the 0.01 level of significance that the mixed nut
> State the null and alternative hypotheses to be used in testing the following claims, and determine generally where the critical region is located: (a) At most, 20% of next year’s wheat crop will be exported to the Soviet Union. (b) On the average, Ameri
> In a study analyzed by the Statistics Consulting Center at Virginia Tech, a group of subjects was asked to complete a certain task on the computer. The response measured was the time to completion. The purpose of the experiment was to test a set of facil
> Consider the situation of Exercise 10.54 on page 360. Oxygen consumption in mL/kg/min, was also measured. It is conjectured that oxygen consumption should be higher in an environment relatively free of CO. Do a significance test and discuss the conject
> The following data are the selling prices z of a certain make and model of used car w years old. Fit a curve of the form μz|w = γδw by means of the nonlinear sample regression equation ˆz = cdw. w (
> A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the “dynamic lift” characteristics of an individual. Twenty-five individuals were subjected to strength t
> The equation used to predict the net sales (in millions of dollars) for a fiscal year for a clothing retailer is y = 23,769 + 9.18x1 - 8.41x2 where x1 is the number of stores open at the end of the fiscal year and x2 is the average square footage per sto
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the percentage of employment in STEM (science, technology, engineering, and mat
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the heights (in feet) and trunk diameters (in inches) of eight trees. The equat
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the number of goals allowed and the total points earned (2 points for a win and
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the median annual earnings (in dollars) of male and female workers from 10 stat
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The numbers of initial public offerings of stock issued and the total proceeds of these offeri
> Match the description in the left column with its symbol(s) in the right column. The y-value of a data point corresponding to xi a. y ̂i b. yi c. b d. (x, y) e. m f. y
> Use the multiple regression equation to predict the y-values for the values of the independent variables. An equation that can be used to predict fuel economy (in miles per gallon) for automobiles is y ̂= 41.3 - 0.004x1 - 0.0049x2 where x1 is the engine
> Match the regression equation with the appropriate graph. y Ì‚= -0.705x + 27.214 а. b. 30 30 25 25 20 20 15 15 10 10 5 5 +++++ ++x 5 10 15 20 25 30 35 40 + 2 4 6 8 10 C. d. y 140 70- 120 60 100 50 80 40 60 30 40 20 20- 10 10 20 30 40 50 5
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result. The table shows the cooking areas (in square inches) of 18 gas grills and their prices (in dol
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result. The table shows the combined city and highway fuel efficiency (in miles per gallon gasoline eq
> Match the regression equation with the appropriate graph. y Ì‚= 2.125x + 9.588 а. b. 30 30 25 25 20 20 15 15 10 10 5 5 +++++ ++x 5 10 15 20 25 30 35 40 + 2 4 6 8 10 C. d. y 140 70- 120 60 100 50 80 40 60 30 40 20 20- 10 10 20 30 40 50 5 1
> Match the regression equation with the appropriate graph. y Ì‚= 2.115x + 21.958 а. b. 30 30 25 25 20 20 15 15 10 10 5 5 +++++ ++x 5 10 15 20 25 30 35 40 + 2 4 6 8 10 C. d. y 140 70- 120 60 100 50 80 40 60 30 40 20 20- 10 10 20 30 40 50 5
> Match the regression equation with the appropriate graph. y Ì‚= -1.361x + 21.952 а. b. 30 30 25 25 20 20 15 15 10 10 5 5 +++++ ++x 5 10 15 20 25 30 35 40 + 2 4 6 8 10 C. d. y 140 70- 120 60 100 50 80 40 60 30 40 20 20- 10 10 20 30 40 50
> Match the description in the left column with its symbol(s) in the right column. Slope a. y ̂i b. yi c. b d. (x, y) e. m f. y
> Match the description in the left column with its symbol(s) in the right column. The point a regression line always passes through a. y ̂i b. yi c. b d. (x, y) e. m f. y
> Match the description in the left column with its symbol(s) in the right column. The mean of the y-values a. y ̂i b. yi c. b d. (x, y) e. m f. y
> a. identify the claim and state H0 and Ha, b. find the critical value(s) and identify the rejection region(s), c. find the standardized test statistic x2, d. decide whether to reject or fail to reject the null hypothesis, and e. interpret the decisio
> Determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim. Claim: p ≥ 0.04; α = 0.10 Sample statistics: p ̂= 0.03, n = 30
> Determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim. Claim: p = 0.65; α = 0.03 Sample statistics: p ̂= 0.76, n = 116
> Determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim. Claim: p = 0.15; α = 0.05 Sample statistics: (p ) ̂= 0.09, n = 40
> Use the multiple regression equation to predict the y-values for the values of the independent variables. The equation used to predict the weight of an elephant (in kilograms) is y ̂= -4016 + 11.5x1 + 7.55x2 + 12.5x3 where x1 represents the girth of the
> Use the multiple regression equation to predict the y-values for the values of the independent variables. The volume (in cubic feet) of a black cherry tree can be modeled by the equation y ̂= -52.2 + 0.3x1 + 4.5x2 where x1 is the tree’s height (in feet)
> Use the multiple regression equation to predict the y-values for the values of the independent variables. The equation used to predict the annual sorghum yield (in bushels per acre) is y ̂= 80.1 - 20.2x1 + 21.2x2 where x1 is the number of acres planted (
> Use the multiple regression equation to predict the y-values for the values of the independent variables. The equation used to predict the annual cauliflower yield (in pounds per acre) is y ̂= 24,791 + 4.508x1 - 4.723x2 where x1 is the number of acres pl
> Match the description in the left column with its symbol(s) in the right column. The y-value for a point on the regression line corresponding to xi a. y ̂i b. yi c. b d. (x, y) e. m f. y
> A researcher collects the data shown below and concludes that there is a significant relationship between the amount of radio advertising time (in minutes per week) and the weekly sales of a product (in hundreds of dollars). Find the standard error of e
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the numbers of new-vehicle sales (in thousands) in the United States for Ford a
> Match the description in the left column with its symbol(s) in the right column. y-intercept a. y ̂i b. yi c. b d. (x, y) e. m f. y
> The regression equation for the Old Faithful data is y ̂= 12.481x + 33.683. Use this to predict the time until the next eruption for each eruption duration. (Recall from Section 9.1, Example 6, that x and y have a significant linear correlation.) 1. 2 mi
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the total assets (in billions of dollars) of individual retirement accounts (IR
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The table shows the amounts of crude oil (in thousands of barrels per day) produced by the Unit
> Find the critical values x_L^2 and x_R^2 for a two-tailed test when n = 51 and α = 0.01.
> Find the critical value x_0^2 for a left-tailed test when n = 30 and α = 0.05
> Find the critical value x_0^2 for a right-tailed test when n = 18 and α = 0.01.
> Use the data to a. find the coefficient of determination r2 and interpret the result, and b. find the standard error of estimate se and interpret the result The U.S. voting age populations (in millions) and the number of ballots cast (in millions) for
> The table shows the metacarpal bone lengths (in centimeters) and the heights (in centimeters) of 12 adults. The equation of the regression line is y Ì‚= 1.707x + 94.380. a. Find the coefficient of determination r2 and interpret the results
> Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. F (x, y, z) = eyz i + xzeyz j + xyeyz k
