For testing H0: μ = 14, H1: μ ≠ 14, an α = 0.05 level t-test is being considered. What sample size is necessary in order for the probability to be 0.1 of falsely failing to reject H0 when the true population mean differs from 14 by 0.5? From a preliminary sample we estimate σ to be 1.25.
> With reference to Exercise 11.1 on page 398, assume that x and y are random variables with a bivariate normal distribution. (a) Calculate r. (b) Test the hypothesis that ρ = 0 against the alternative that ρ = 0 at the 0.05 level of
> Compute and interpret the correlation coefficient for the following grades of 6 students selected at random: Mathematics grade 70 92 80 74 65 83 English grade 74 84 63 87 78 90
> For a particular variety of plant, researchers wanted to develop a formula for predicting the quantity of seeds (in grams) as a function of the density of plants. They conducted a study with four levels of the factor x, the number of plants per plot. Fou
> Evaluating nitrogen deposition from the atmosphere is a major role of the National Atmospheric Deposition Program (NADP), a partnership of many agencies. NADP is studying atmospheric deposition and its effect on agricultural crops, forest surface waters,
> It is of interest to study the effect of population size in various cities in the United States on ozone concentrations. The data consist of the 1999 population in millions and the amount of ozone present per hour in ppb (parts per billion). The data are
> The following data were collected to determine the relationship between pressure and the corresponding scale reading for the purpose of calibration. (a) Find the equation of the regression line. (b) The purpose of calibration in this application is to
> A regression model is desired relating temperature and the proportion of impurities passing through solid helium. Temperature is listed in degrees centigrade. The data are as follows: (a) Fit a linear regression model. (b) Does it appear that the propo
> Heat treating is often used to carburize metal parts such as gears. The thickness of the carburized layer is considered an important feature of the gear, and it contributes to the overall reliability of the part. Because of the critical nature of this fe
> Organophosphate (OP) compounds are used as pesticides. However, it is important to study their effect on species that are exposed to them. In the laboratory study Some Effects of Organophosphate Pesticides on Wildlife Species, by the Department of Fisher
> Transistor gain between emitter and collector in an integrated circuit device (hFE) is related to two variables (Myers, Montgomery and Anderson-Cook, 2009) that can be controlled at the deposition process, emitter drive-in time (x1, in minutes) and emitt
> The following data are a result of an investigation as to the effect of reaction temperature x on percent conversion of a chemical process y. (See Myers, Montgomery and Anderson-Cook, 2009.) Fit a simple linear regression, and use a lack-of-fit test to d
> Use an analysis-of-variance approach to test the hypothesis that β1 = 0 against the alternative hypothesis β1 = 0 in Exercise 11.5 on page 398 at the 0.05 level of significance. Exercise 11.5: A study was made on the amount of co
> Suppose we have a linear equation through the origin (Exercise 11.28) μY |x = βx. (a) Estimate the regression line passing through the origin for the following data: (b) Suppose it is not known whether the true regression shou
> Test for linearity of regression in Exercise 11.8 on page 399. Comment. Exercise 11.8: A mathematics placement test is given to all entering freshmen at a small college. A student who receives a grade below 35 is denied admission to the regular mathemat
> Test for linearity of regression in Exercise 11.3 on page 398. Use a 0.05 level of significance. Comment. Exercise 11.3: The amounts of a chemical compound y that dissolved in 100 grams of water at various temperatures x were recorded as follows: (a)
> For the data in Exercise 11.29, find a 95% prediction interval at x = 25.
> The amounts of a chemical compound y that dissolved in 100 grams of water at various temperatures x were recorded as follows: (a) Find the equation of the regression line. (b) Graph the line on a scatter diagram. (c) Estimate the amount of chemical tha
> Use the data set (a) Plot the data. (b) Fit a regression line through the origin. (c) Plot the regression line on the graph with the data. (d) Give a general formula (in terms of the yi and the slope b1) for the estimator of σ2. (e) Give a f
> There are important applications in which due to known scientific constraints, the regression line must go through the origin (i.e., the intercept must be zero). In other words, the model should read and only a simple parameter requires estimation. The
> Consider the regression of mileage for certain automobiles, measured in miles per gallon (mpg) on their weight in pounds (wt). The data are from Consumer Reports (April 1997). Part of the SAS output from the procedure is shown in Figure 11.13. (a) Estim
> With reference to Exercise 11.3 on page 398, use the value of s2 found in Exercise 11.19(a) to compute (a) a 99% confidence interval for the average amount of chemical that will dissolve in 100 grams of water at 50 â—¦ C; (b) a 99% pred
> Using the value of s2 found in Exercise 11.17(a), construct a 95% confidence interval for the amount of converted sugar corresponding to x = 1.6 in Exercise 11.5 on page 398. Exercise 11.17: With reference to Exercise 11.5 on page 398, (a) evaluate s2;
> Using the value of s2 found in Exercise 11.17(a), graph the regression line and the 95% confidence bands for the mean response μY |x for the data of Exercise 11.5 on page 398. Exercise 11.17: With reference to Exercise 11.5 on page 398, (a
> With reference to Exercise 11.6 on page 399, use the value of s2 found in Exercise 11.18(a) to compute (a) a 95% confidence interval for the mean shear resistance when x = 24.5; (b) a 95% prediction interval for a single predicted value of the shear resi
> Using the value of s2 found in Exercise 11.16(a), construct a 95% confidence interval for μY |85 in Exercise 11.2 on page 398. Exercise 11.16: With reference to Exercise 11.2 on page 398, (a) evaluate s2; (b) construct a 95% confidence interval for β0;
> Test the hypothesis that β1 = 6 in Exercise 11.9 on page 399 against the alternative that β1 Use a 0.025 level of significance. Exercise 11.9: A study was made by a retail merchant to determine the relation between weekly adverti
> Test the hypothesis that β0 = 10 in Exercise 11.8 on page 399 against the alternative that β0 Exercise 11.8: A mathematics placement test is given to all entering freshmen at a small college. A student who receives a grade below
> The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: x 77 50 71 72 81 94 96 99 67 y 82 66 78 34 47 85 99 99 68 (a) Estimate the linear regression line. (b) Estimate the final examination grade of a
> With reference to Exercise 11.3 on page 398, (a) evaluate s2; (b) construct a 99% confidence interval for β0; (c) construct a 99% confidence interval for β1. Exercise 11.3: The amounts of a chemical compound y that dissolved in 1
> With reference to Exercise 11.6 on page 399, (a) evaluate s2; (b) construct a 99% confidence interval for β0; (c) construct a 99% confidence interval for β1. Exercise 11.6: In a certain type of metal test specimen, the normal str
> A dry cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 12 spots chosen at random. If fewer than 11 of the spots are removed, we shal
> In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced by a particular species of mussel found off the coast of New
> Repeat Exercise 10.6 but assume that 200 adults are selected and the fail-to-reject region is defined to be 110 ≤ x ≤ 130, where x is the number of college graduates in our sample. Use the normal approximation. Exercise 10.6: The proportion of adults li
> An urban community would like to show that the incidence of breast cancer is higher in their area than in a nearby rural area. (PCB levels were found to be higher in the soil of the urban community.) If it is found that 20 of 200 adult women in the urban
> In a study on the fertility of married women conducted by Martin O’Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of childless wives aged 25 to 29 were selected at random, and each was asked if she eventually planned to have a ch
> In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in fav
> In a controlled laboratory experiment, scientists at the University of Minnesota discovered that 25% of a certain strain of rats subjected to a 20% coffee bean diet and then force-fed a powerful cancer-causing chemical later developed cancerous tumors. W
> With reference to Exercise 11.5 on page 398, (a) evaluate s2; (b) construct a 95% confidence interval for β0; (c) construct a 95% confidence interval for β1. Exercise 11.5: A study was made on the amount of converted sugar in a c
> In a winter of an epidemic flu, the parents of 2000 babies were surveyed by researchers at a wellknown pharmaceutical company to determine if the company’s new medicine was effective after two days. Among 120 babies who had the flu and were given the med
> At a certain college, it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class? Use a 0.05 level of significance.
> The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 6 to 12, we shall n
> A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than one-fifth are heated by oil if, in a random sample of 1000 homes in this city, 136 are heated by oil? Use a P-value in
> It is believed that at least 60% of the residents in a certain area favor an annexation suit by a neighboring city. What conclusion would you draw if only 110 in a sample of 200 voters favored the suit? Use a 0.05 level of significance.
> A new radar device is being considered for a certain missile defense system. The system is checked by experimenting with aircraft in which a kill or a no kill is simulated. If, in 300 trials, 250 kills occur, accept or reject, at the 0.04 level of signif
> Suppose that, in the past, 40% of all adults favored capital punishment. Do we have reason to believe that the proportion of adults favoring capital punishment has increased if, in a random sample of 15 adults, 8 favor capital punishment? Use a 0.05 leve
> A marketing expert for a pasta-making company believes that 40% of pasta lovers prefer lasagna. If 9 out of 20 pasta lovers choose lasagna over other pastas, what can be concluded about the expert’s claim? Use a 0.05 level of significance.
> Nine subjects were used in an experiment to determine if exposure to carbon monoxide has an impact on breathing capability. The data were collected by personnel in the Health and Physical Education Department at Virginia Tech and were analyzed in the Sta
> A study was conducted at the Department of Veterinary Medicine at Virginia Tech to determine if the “strength” of a wound from surgical incision is affected by the temperature of the knife. Eight dogs were used in the
> With reference to Exercise 11.2 on page 398, (a) evaluate s2; (b) construct a 95% confidence interval for β0; (c) construct a 95% confidence interval for β1. Exercise 11.2: The grades of a class of 9 students on a midterm report (x) and on the final exa
> How large a sample is required in Exercise 10.22 if the power of the test is to be 0.8 when the true mean meditation time exceeds the hypothesized value by 1.2σ? Use α = 0.05. Exercise 10.22: In the American Heart Association journal Hypertension, resea
> How large should the samples be in Exercise 10.31 if the power of the test is to be 0.95 when the true difference between thread types A and B is 8 kilograms? Exercise 10.31: A manufacturer claims that the average tensile strength of thread A exceeds th
> Repeat Exercise 10.4 but assume that 50 orders are selected and the critical region is defined to be x ≤ 24, where x is the number of orders in the sample that arrived late. Use the normal approximation. Exercise 10.4: A fabric manufacturer believes tha
> 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.
