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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions

In a study to establish the absolute threshold of hearing, 70 male college freshmen were asked to participate. Each subject was seated in a soundproof room and a 150 H tone was presented at a large number of stimulus levels in a randomized order. The subject was instructed to press a button if he
A researcher classified his subjects as innately right-handed or left-handed by comparing thumbnail widths. He took a sample of 400 men and found that 80 men could be classified as left-handed according to his criterion. Estimate the proportion of all males in the population who would test to be
An entomologist wishes to estimate the average development time of the citrus red mite correct to within .5 day. From previous experiments it is known that σ is approximately 4 days. How large a sample should the entomologist take to be 95% confident of her estimate?
A grower believes that one in five of his citrus trees are infected with the citrus red mite mentioned in Exercise 8.116. How large a sample should be taken if the grower wishes to estimate the proportion of his trees that are infected with citrus red mite to within .08?
A random sample of n = 50 observations from a quantitative population produced = 56.4 and s2 = 2.6. Give the best point estimate for the population mean m, and calculate the margin of error.
A random sample of n = 500 observations from a binomial population produced x = 450 successes. Estimate the binomial proportion p and calculate the margin of error.
A random sample of n = 75 observations from a quantitative population produced = 29.7 and s2 = 10.8. Give the best point estimate for the population mean µ and calculate the margin of error.
One of the most famous large fractures (cracks) in the earth's crust is the San Andreas fault in California. A geologist attempting to study the movement of the earth's crust at a particular location found many fractures in the local rock structure. In an attempt to determine the mean angle of the
Estimates of the earth's biomass, the total amount of vegetation held by the earth's forests, are important in determining the amount of unabsorbed carbon dioxide that is expected to remain in the earth's atmosphere. Suppose a sample of 75 one-square-meter plots, randomly chosen in North America's
An increase in the rate of consumer savings is frequently tied to a lack of confidence in the economy and is said to be an indicator of a recessional tendency in the economy. A random sampling of n = 200 savings accounts in a local community showed a mean increase in savings account values of 7.2%
Do our children spend as much time enjoying the outdoors and playing with family and friends as previous generations did? Or are our children spending more and more time glued to the television, computer, and other multimedia equipment? A random sample of 250 children between the ages of 8 and 18
In a recent poll that included questions about illegal immigration into the United States, and the federal and state responses to the problem, 75% of the n = 1004 adults surveyed felt that the United States is not doing enough to keep illegal immigrants from coming into this country. a. What is a
Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Marriott, Westin, and the Doubletree hotel
Radio and television stations often air controversial issues during broadcast time and ask viewers to indicate their agreement or disagreement with a given stand on the issue. A poll is conducted by asking those viewers who agree to call a certain 900 telephone number and those who disagree to call
Do you think that the United States should pursue a program to send humans to Mars? An opinion poll conducted by the Associated Press indicated that 49% of the 1034 adults surveyed think that we should pursue such a program. a. Estimate the true proportion of Americans who think that the United
In an experiment to assess the strength of the hunger drive in rats, 30 previously trained animals were deprived of food for 24 hours. At the end of the 24-hour period, each animal was put into a cage where food was dispensed if the animal pressed a lever. The length of time the animal continued
Find and interpret a 95% confidence interval for a population mean µ for these values: a. n = 36, = 13.1, s2 = 3.42 b. n = 64, = 2.73, s2 = .1047
Find a 90% confidence interval for a population mean µ for these values: a. n = 125, = .84, s2 = .086 b. n = 50, = 21.9, s2 = 3.44 c. Interpret the intervals found in parts a and b.
Find a (1 - α) 100% confidence interval for a population mean µ for these values: a. α = .01, n = 38, = 34, s2 = 12 b. α = .10, n = 65, = 1049, s2 = 51 c. α = .05, n = 89, = 66.3, s2 = 2.48
A random sample of n = 300 observations from a binomial population produced x = 263 successes. Find a 90% confidence interval for p and interpret the interval.
Suppose the number of successes observed in n = 500 trials of a binomial experiment is 27. Find a 95% confidence interval for p. Why is the confidence interval narrower than the confidence interval in Exercise 8.27?
A random sample of n measurements is selected from a population with unknown mean µ and known standard deviation σ = 10. Calculate the width of a 95% confidence interval for µ for these values of n: a. n = 100 b. n = 200 c. n = 400
Calculate the margin of error in estimating a population mean µ for these values: a. n = 30, σ2 = .2 b. n = 30, σ2 = .9 c. n = 30, σ2 = 1.5
Compare the confidence intervals in Exercise 8.29. What effect does each of these actions have on the width of a confidence interval? a. Double the sample size b. Quadruple the sample size
Refer to Exercise 8.30. a. Calculate the width of a 90% confidence interval for m when n = 100. b. Calculate the width of a 99% confidence interval for m when n = 100. c. Compare the widths of 90%, 95%, and 99% confidence intervals for µ. What effect does increasing the confidence coefficient have
In an electrolysis experiment, a class measured the amount of copper precipitated from a saturated solution of copper sulfate over a 30-minute period. The n = 30 students calculated a sample mean and standard deviation equal to .145 and .0051 mole, respectively. Find a 90% confidence interval for
Acid rain, caused by the reaction of certain air pollutants with rainwater, is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). Suppose water samples from 40 rainfalls are analyzed for
In an Advertising Age white paper concerning the changing role of women as "breadwinners" in the American family, it was reported that according to their survey with JWT, working men reported doing 54 minutes of household chores a day, while working women reported tackling 72 minutes daily. But
The meat department of a local supermarket chain packages ground beef using meat trays of two sizes: one designed to hold approximately 1 pound of meat, and one that holds approximately 3 pounds. A random sample of 35 packages in the smaller meat trays produced weight measurements with an average
The results of a CBS News Poll concerning views on same-sex marriage and gay rights given in Exercise 7.68 showed that of n = 1082 adults, 40% favored legal marriage, 30% favored civil unions, and 25% believed there should be no legal recognition. The poll reported a margin of error of plus or
A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A random sample of 500 registrations are selected from a Department of Motor Vehicles database, and 68 are classified as sports utility vehicles. a. Use a 95% confidence
New car models with names such as the "Volt" and the "Leaf" are being hyped by automakers, as they scramble to produce electric cars that are affordable for most Americans. Still in the trial stage, BMW's Mini E can be leased for about $600 per month, and is claimed to be able to travel between 100
What is normal, when it comes to people's body temperatures? A random sample of 130 human body temperatures, provided by Allen Shoemaker in the Journal of Statistical Education, had a mean of 98.25° and a standard deviation of 0.73°. a. Construct a 99% confidence interval for the average body
How likely are you to vote in the next national election? In a survey by Pew Research, fully 77% of the registered Republican voters are absolutely going to vote this year while only 65% of Democrats are absolutely going to vote in the next election. The sample consisted of 469 registered
Independent random samples were selected from populations 1 and 2. The sample sizes, means, and variances are as follows:a. Find a 95% confidence interval for estimating the difference in the population means (µ1 - µ2). b. Based on the confidence interval in part a, can you conclude
Independent random samples were selected from populations 1 and 2. The sample sizes, means, and variances are as follows:a. Find a 90% confidence interval for the difference in the population means. What does the phrase "90% confident" mean?b. Find a 99% confidence interval for the difference in
Independent random samples of size n1 = n2 = 100 were selected from each of two populations. The mean and standard deviations for the two samples were 1 = 125.2, 2 = 123.7, s1 = 5.6, and s2 = 6.8. a. Construct a 99% confidence interval for estimating the difference in the two population means. b.
Independent random samples of size n1 = n2 = 500 were selected from each of two populations. The mean and standard deviations for the two samples were 1 = 125.2, 2 = 123.7, s1 = 5.6, and s2 = 6.8.a. Find a point estimate for the difference in the two population means. Calculate the margin of
A small amount of the trace element selenium, 50-200 micrograms (mg) per day, is considered essential to good health. Suppose that random samples of n1 = n2 = 30 adults were selected from two regions of the United States and that a day's intake of selenium was recorded for each person. The mean and
A study was conducted to compare the mean numbers of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions, and the number of emergency calls was recorded for each shift. The
An experiment was conducted to compare a teacher-developed curriculum, "Biology: A Community Context" (BACC) that was standards-based, activity-oriented, and inquiry-centered to the traditional presentation using lecture, vocabulary, and memorized facts. The perhaps not-so startling results when
To compare two weight reduction diets A and B, 60 dieters were randomly selected. One group of 30 dieters was placed on diet A and the other 30 on diet B, and their weight losses were recorded over a 30-day period. The means and standard deviations of the weight-loss measurements for the two groups
As a group, students majoring in the engineering disciplines have the highest salary expectations, followed by those studying the computer science fields, according to results of NACE's 2010 Student Survey. To compare the starting salaries of college graduates majoring in engineering and computer
Calculate the margin of error in estimating a population mean µ for these values: a. n = 50, s2 = 4 b. n = 500, s2 = 4 c. n = 5000, s2 = 4
Refer to Exercise 8.47. In addition to tests involving biology concepts, students were also tested on process skills. The results of pretest and posttest scores, published in The American Biology Teacher, are given below.a. Find a 95% confidence interval for the mean score on process skills for the
Refer to Exercise 8.20. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table:a. Find a 95% confidence interval for the difference in the average room rates for the Marriott and the Westin hotel
To compare the effect of stress in the form of noise on the ability to perform a simple task, 70 subjects were divided into two groups. The first group of 30 subjects acted as a control, while the second group of 40 were the experimental group. Although each subject performed the task, the
Of the 130 people in Exercise 8.39, 65 were female and 65 were male. The means and standard deviation of their temperatures are shown below.Find a 95% confidence interval for the difference in the average body temperatures for males versus females. Based on this interval, can you conclude that
Independent random samples of n1 = 500 and n2 = 500 observations were selected from binomial populations 1 and 2, and x1 = 120 and x2 = 147 successes were observed.a. What is the best point estimator for the difference (p1 - p2) in the two binomial proportions?b. Calculate the approximate standard
Independent random samples of n1 = 800 and n2 = 640 observations were selected from binomial populations 1 and 2, and x1 = 337 and x2 = 374 successes were observed.a. Find a 90% confidence interval for the difference (p1 - p2) in the two population proportions. Interpret the interval.b. What
Independent random samples of n1 = 1265 and n2 = 1688 observations were selected from binomial populations 1 and 2, and x1 = 849 and x2 = 910 successes were observed.a. Find a 99% confidence interval for the difference (p1 - p2) in the two population proportions. What does "99% confidence" mean?b.
Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 56 plain M&M'S contained 12 red candies, and another random sample of 32 peanut M&M'S contained 8 red candies.a. Construct a 95% confidence interval for the difference in the
As we approached the midterm elections, in the summer of 2010, Democrats and Republicans were split about our nation's top priorities. A sample of n = 900 registered voters were asked the following question: "Which ONE of the following items do you think is most important for the federal government
The first day of baseball comes in late March, ending in October with the World Series. Does fan support grow as the season goes on? Two CNN/USA Today/Gallup polls, one conducted in March and one in November, both involved random samples of 1001 adults aged 18 and older. In the March sample, 45% of
According to a national representative survey done by Consumer Reports, you should always try to negotiate for a better deal when shopping or paying for services. Tips include researching prices at other stores and on the Internet, timing your visit late in the month when sales-people are trying to
Do well-rounded people get fewer colds? A study on the Chronicle of Higher Education was conducted by scientists at Carnegie Mellon University, the University of Pittsburgh, and the University of Virginia. They found that people who have only a few social outlets get more colds than those who are
A sampling of political candidates-200 randomly chosen from the West and 200 from the East-was classified according to whether the candidate received backing by a national labor union and whether the candidate won. In the West, 120 winners had union backing, and in the East, 142 winners were backed
In a study of the relationship between birth order and college success, an investigator found that 126 in a sample of 180 college graduates were firstborn or only children. In a sample of 100 non-graduates of comparable age and socioeconomic background, the number of firstborn or only children was
Born between 1980 and 1990, Generation Next is engaged with technology, and the vast majority is dependent upon it. Suppose that in a survey of 500 female and 500 male students in Generation Next, 345 of the females and 365 of the males reported that they decided to attend college in order to make
In a study to compare the effects of two pain relievers it was found that of n1 = 200 randomly selected individuals who used the first pain reliever, 93% indicated that it relieved their pain. Of n2 = 450 randomly selected individuals who used the second pain reliever, 96% indicated that it
Last year's records of auto accidents occurring on a given section of highway were classified according to whether the resulting damage was $1000 or more and to whether a physical injury resulted from the accident. The data follows:a. Estimate the true proportion of accidents involving injuries
Find a 90% one-sided upper confidence bound for the population mean µ for these values: a. n = 40, s2 = 65, = 75 b. n = 100, s = 2.3, = 1.6
Find a 99% lower confidence bound for the binomial proportion p when a random sample of n = 400 trials produced x = 196 successes.
Independent random samples of size 50 are drawn from two quantitative populations, producing the sample information in the table. Find a 95% upper confidence bound for the difference in the two population means.
Calculate the margin of error in estimating a binomial proportion for each of the following values of n. Use p = .5 to calculate the standard error of the estimator. a. n = 30 b. n = 100 c. n = 400 d. n = 1000
Suppose you wish to estimate a population mean based on a random sample of n observations, and prior experience suggests that σ = 12.7. If you wish to estimate µ correct to within 1.6, with probability equal to .95, how many observations should be included in your sample?
Suppose you wish to estimate a binomial parameter p correct to within .04, with probability equal to .95. If you suspect that p is equal to some value between .1 and .3 and you want to be certain that your sample is large enough, how large should n be?
Independent random samples of n1 = n2 = n observations are to be selected from each of two populations 1 and 2. If you wish to estimate the difference between the two population means correct to within .17, with probability equal to .90, how large should n1 and n2 be? Assume that you know σ21 ≈
Independent random samples of n1 = n2 = n observations are to be selected from each of two binomial populations 1 and 2. If you wish to estimate the difference in the two population proportions correct to within .05, with probability equal to .98, how large should n be? Assume that you have no
A random sampling of a company's monthly operating expenses for n = 36 months produced a sample mean of $5474 and a standard deviation of $764. Find a 90% upper confidence bound for the company's mean monthly expenses.
Exercise 8.19 discussed a research poll conducted for ABC News and the Washington Post that included questions about illegal immigration into the United States, and the federal and state responses to the problem. Suppose that you were designing a poll of this type. a. Explain how you would select
A questionnaire is designed to investigate attitudes about political corruption in government. The experimenter would like to survey two different groups-Republicans and Democrats-and compare the responses to various "yes/no" questions for the two groups. The experimenter requires that the sampling
As Americans become more conscious of the importance of good nutrition, some researchers believe that we may be eating less red meat. To test this theory, a researcher decides to select hospital nutritional records for subjects surveyed 10 years ago and to compare the average amount of beef
Refer to Exercise 8.77. The researcher selects two groups of 400 subjects each and collects the following sample information on the annual beef consumption now and 10 years ago:a. The researcher would like to show that per-capita beef consumption has decreased in the last 10 years, so she needs to
A wildlife service wishes to estimate the mean number of days of hunting per hunter for all hunters licensed in the state during a given season. How many hunters must be included in the sample in order to estimate the mean with a bound on the error of estimation equal to 2 hunting days? Assume that
Suppose you wish to estimate the mean pH of rainfalls in an area that suffers heavy pollution due to the discharge of smoke from a power plant. You know that σ is approximately .5 pH, and you wish your estimate to lie within .1 of µ, with a probability near .95. Approximately how many rainfalls
Refer to Exercise 8.80. Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If you wish your estimate to be correct to the nearest .1 pH, with
You want to estimate the difference in grade point averages between two groups of college students accurate to within .2 grade point, with probability approximately equal to .95. If the standard deviation of the grade point measurements is approximately equal to .6, how many students must be
Refer to the comparison of the daily adult intake of selenium in two different regions of the United States in Exercise 8.45. Suppose you wish to estimate the difference in the mean daily intakes between the two regions correct to within 5 micrograms, with probability equal to .90. If you plan to
A random sample of n = 64 observations has a mean = 29.1 and a standard deviation s = 3.9.a. Give the point estimate of the population mean µ and find the margin of error for your estimate.b. Find a 90% confidence interval for µ. What does "90% confident" mean?c. Find a 90% lower confidence
Independent random samples of n1 = 50 and n2 = 60 observations were selected from populations 1 and 2, respectively. The sample sizes and computed sample statistics are given in the table:Find a 90% confidence interval for the difference in population means and interpret the interval.
Refer to Exercise 8.86. Suppose you wish to estimate (µ1 - µ2) correct to within .2, with probability equal to .95. If you plan to use equal sample sizes, how large should n1 and n2 be?Exercise 8.86Independent random samples of n1 = 50 and n2 = 60 observations were selected from
A random sample of n = 500 observations from a binomial population produced x = 240 successes. a. Find a point estimate for p, and find the margin of error for your estimator. b. Find a 90% confidence interval for p. Interpret this interval.
Refer to Exercise 8.88. How large a sample is required if you wish to estimate p correct to within .025, with probability equal to .90? Exercise 8.88 A random sample of n = 500 observations from a binomial population produced x = 240 successes.
Calculate the margin of error in estimating a binomial proportion p using samples of size n = 100 and the following values for p: a. p = .1 b. p = .3 c. p = .5 d. p = .7 e. p = .9 f. Which of the values of p produces the largest margin of error?
Independent random samples of n1 = 40 and n2 = 80 observations were selected from binomial populations 1 and 2, respectively. The number of successes in the two samples were x1 = 17 and x2 = 23. Find a 99% confidence interval for the difference between the two binomial population proportions.
Refer to Exercise 8.90. Suppose you wish to estimate (p1 - p2) correct to within .06, with probability equal to .99, and you plan to use equal sample sizes- that is, n1 = n2. How large should n1 and n2 be? Exercise 8.90 Independent random samples of n1 = 40 and n2 = 80 observations were selected
Ethnic groups in America buy differing amounts of various food products because of their ethnic cuisine. A researcher interested in market segmentation for Asian and Hispanic households would like to estimate the proportion of households that select certain brands for various products. If the
In Exercise 8.60, a survey done by Consumer Reports indicates that you should always try to negotiate for a better deal when shopping or paying for services.15 In fact, based on their survey, 37% of the people under age 34 were more likely to "haggle," while only 13% of those 65 and older. Suppose
An experiment was conducted to estimate the effect of smoking on the blood pressure of a group of 35 cigarette smokers, by taking the difference in the blood pressure readings at the beginning of the experiment and again 5 years later. The sample mean increase, measured in millimeters of mercury,
Using a confidence coefficient equal to .90, place a confidence interval on the mean increase in blood pressure for Exercise 8.94.
Based on repeated measurements of the iodine concentration in a solution, a chemist reports the concentration as 4.614, with an "error margin of .006." a. How would you interpret the chemist's "error margin"? b. If the reported concentration is based on a random sample of n = 30 measurements, with
If it is assumed that the heights of men are normally distributed with a standard deviation of 2.5 inches, how large a sample should be taken to be fairly sure (probability .95) that the sample mean does not differ from the true mean (population mean) by more than .50 in absolute value?
An experimenter fed different rations, A and B, to two groups of 100 chicks each. Assume that all factors other than rations are the same for both groups. Of the chicks fed ration A, 13 died, and of the chicks fed ration B, 6 died.a. Construct a 98% confidence interval for the true difference in
You want to estimate the mean hourly yield for a process that manufactures an antibiotic. You observe the process for 100 hourly periods chosen at random, with the results = 34 ounces per hour and s = 3. Estimate the mean hourly yield for the process using a 95% confidence interval.
When Americans eat out at restaurants, most choose American food; however, tastes for Mexican, Chinese, and Italian food vary from region to region of the United States. In a recent CBS telephone survey, it was found that 39% of families ate together 7 nights a week, slightly less than the 46% of
Find the appropriate rejection regions for the large-sample test statistic z in these cases: a. A right-tailed test with α = .01 b. A two-tailed test at the 5% significance level.
Suppose a scheduled airline flight must average at least 60% occupancy in order to be profitable to the airline. An examination of the occupancy rate for 120 10:00 A.M. flights from Atlanta to Dallas showed a mean occupancy per flight of 58% and a standard deviation of 11%. a. If µ is the mean
Exercise 8.35 involved packages of ground beef in a small tray, intended to hold 1 pound of meat. A random sample of 35 packages in the small tray produced weight measurements with an average of 1.01 pounds and a standard deviation of .18 pound. a. If you were the quality control manager and wanted
In a study of the pernicious giant hogweed, Jan Pergl1 and associates compared the density of these plants in two different sites within the Caucasus region of Russia. In its native area, the average density was found to be 5 plants/m2. In an invaded area in the Czech Republic, a sample of n = 50

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