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introduction to probability statistics
Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions
9.69 Losing Weight In a comparison of the mean 1-month weight losses for women aged 20 to 30 years, these sample data were obtained for each of two diets:Do the data provide sufficient evidence to indicate that diet I produces a greater mean weight loss than diet II? Use = 0.05. Diet I Diet II
9.70 Increased Yield An agronomist has shown experimentally that a new irrigation/fertilization regimen produces an increase of 17,635 cm per quadrant (significant at the 1% level) when compared with the regimen currently in use. The cost of implementing and using the new regimen will not be a
9.71 Breaking Strengths of Cables A test of the breaking strengths of two different types of cables was conducted using samples of n = n = 100 pieces of each type of cable.Do the data provide sufficient evidence to indicate a difference between the mean breaking strengths of the two cables? Use a =
9.72 Put on the Brakes The braking ability was compared for two 2012 automobile models. Random samples of 64 automobiles were tested for each type. The recorded measurement was the distance (in metres) required to stop when the brakes were applied at 65 kilometres per hour (km/hr). These are the
9.73 Spraying Fruit Trees A fruit grower wants to test a new spray that a manufacturer claims will reduce the loss due to insect damage. To test the claim, the grower sprays 200 trees with the new spray and 200 other trees with the standard spray. The following data were recorded:Â a. Do the data
9.74 Actinomycin D A biologist hypothesizes that high concentrations of actinomycin D inhibit RNA synthesis in cells and hence the production of pro- teins as well. An experiment conducted to test this theory compared the RNA synthesis in cells treated with two concentrations of actinomycin D: 0.6
9.75 LSAT Ethnicity and Law The Law School Admissions Test (LSAT) is a multiple-choice test that most (at least those in North America) prospec- tive law students must take in order to apply for law school. The test comprises five 35-minute-long sections. The LSAT score is a three-digit number
9.76 A Maze Experiment In a maze running study, a rat is run in a T maze and the result of each run recorded. A reward in the form of food is always placed at the right exit. If learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place,
9.77 PCBs Polychlorinated biphenyls (PCBs) have been found to be dangerously high in some game birds found along the marshlands of the southeastern coast of North America. A concentration of PCBs higher than 5 parts per million (ppm) in these game birds is considered to be dangerous for human
9.78 PCBs, continued Refer to Exercise 9.77.a. Calculate and 1- if the true mean ppm of PCBs is 6 ppm.b. Calculate and 1- if the true mean ppm of PCBs is 7 ppm.c. Find the power, 1-B, when u 8, 9, 10, and 12. Use these values to construct a power curve for the test in Exercise 9.77.d. For what
9.79 Stricter Emission Standards An Ipsos Reid survey conducted on behalf of Can West/Global Television shows that 68% of Canadians support the view that as Canada's largest producer of oil and gas, Alberta should be subjected to stricter emission stan- dards even if it means a significant increase
9.80 Heights and Gender It is a well-accepted fact that males are taller on average than females. But how much taller? The heights and genders of 105 bio- medical students were recorded and the data are sum- marized below:a. Perform a test of hypothesis to either confirm or refute our initial claim
9.81 Right Number of Immigrants The Strategic Counsel conducted a survey in 2005 for the Globe and Mail/CTV August polling program. The following question was posed to randomly selected Canadians. "Does Canada accept the right number of immigrants per year?" The results are shown in the table.Does
9.82 Breaststroke Swimmers How much training time does it take to become a world-class breaststroke swimmer? A survey published in The American Journal of Sports Medicine reported the number of metres per week swum by two groups of swimmers- those who competed only in breaststroke and those who
9.83 Breaststroke, continued Refer to Exercise 9.82.a. Construct a 99% confidence interval for the dif- ference in the average number of metres swum by breaststroke versus individual medley swimmers.b. How much longer do pure breaststroke swimmers practice that stroke than individual medley swim-
1. Test whether each study, analyzed separately, supports the hypothesis that the gin- seng extract reduces the likelihood of laboratory-confirmed influenza.Edmonton company CV Technologies Inc. has conducted clinical trials, with results published in the Journal of the American Geriatrics Society
2. Repeat your analysis using the pooled data from the two studies.Edmonton company CV Technologies Inc. has conducted clinical trials, with results published in the Journal of the American Geriatrics Society showing that their propri- etary ginseng extract can prevent colds. It obtained results
3. Should it matter to the analysis whether the original endpoint was symptomatic or laboratory-confirmed respiratory illness? How about whether or not the researchers originally intended to conduct two studies and pool the results? Does the data care what the researchers were thinking?Edmonton
Lung cancer remains the leading cause of cancer death for both Canadian men and women, responsible for the most potential years of life lost to cancer. Lung cancer alone accounts for 28% of all cancer deaths in Canada (32% in Quebec). Most forms of lung cancer start insidiously and produce no
Walking is perhaps the simplest exercise you can do anytime it fits in your busy sched- ule. Further it can be viewed as one of the most economical methods of transportation. More importantly, walking reduces the risk of coronary disease. Walking speed varies quite a bit, depending on stride
How to Estimate a Population Mean or Proportion
How to Choose the Sample Size
The circuits in computers and other electronics equipment consist of one or more printed circuit boards (PCB), and computers are often repaired by simply replacing one or more defective PCBs. In an attempt to find the proper setting of a plating process applied to one side of a PCB, a production
The supervisor in Example 8.1 is told by the plant owner that the thickness of the cop- per plating must not be less than 0.003 centimetre (cm) in order for the process to be in control. To decide whether or not the process is in control, the supervisor might formulate a test. He could hypothesize
A veterinarian wants to estimate the average weight gain per month of four-month-old golden retriever pups that have been placed on a lamb and rice diet. The population consists of the weight gains per month of all four-month-old golden retriever pups that are given this particular diet. The
An investigator is interested in the possibility of merging the capabilities of television and the Internet. A random sample of n = 50 Internet users who were polled about the time they spend watching television produced an average of 11.5 hours per week, with a standard deviation of 3.5 hours. Use
In addition to the average time Internet users spend watching television, the researcher from Example 8.4 is interested in estimating the proportion of individuals in the popu- lation at large who want to purchase a television that also acts as a computer. In a random sample of n = 100 adults, 45%
8.1 Explain what is meant by "margin of error" in point estimation.
8.2 What are two characteristics of the best point estimator for a population parameter?
8.3 Calculate the margin of error in estimating a population mean for these values:a. n = 30,0 = 0.2b. n 30, 0.9c. n = 30,0 = 1.5
8.4 Refer to Exercise 8.3. What effect does a larger population variance have on the margin of error?
8.5 Calculate the margin of error in estimating a population mean for these values:a. n = 50, s = 4b. n = 500, s = 4c. n = 5000, s 4
8.6 Refer to Exercise 8.5. What effect does an increased sample size have on the margin of error?
8.7 Calculate the margin of error in estimating a binomial proportion for each of the following values of n. Use p = 0.5 to calculate the standard error of the estimator.a. n = 30c. n = 400b. n = 100d. n = 1000
8.8 Refer to Exercise 8.7. What effect does increasing the sample size have on the margin of error?
8.9 Calculate the margin of error in estimating a bino- mial proportion p using samples of size n = 100 and the following values for p:a. p = 0.1d. p = 0.7b. p = 0.3c. p = 0.5e. p = 0.9f. Which of the values of p produces the largest mar- gin of error?
8.11 A random sample of n = 900 observations from a binomial population produced x = 655 successes. Estimate the binomial proportion p and calculate the margin of error.
8.12 A random sample of n = 50 observations from a quantitative population produced x = 56.4 and = 2.6. Give the best point estimate for the popula- tion mean , and calculate the margin of error.
8.13 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.
8.14 A random sample of n = 75 observations from a quantitative population produced x = 29.7 and 2: 10.8. Give the best point estimate for the population mean and calculate the margin of error.
8.15 The San Andreas Fault Geologists are inter- ested in shifts and movements of the earth's surface indicated by fractures (cracks) in the earth's crust. One of the most famous large fractures is the San Andreas fault in California. A geologist attempting to study the movement of the relative
8.16 Biomass 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-metre plots, randomly chosen in
8.17 Consumer Confidence An increase in the rate of consumer savings is frequently tied to a lack of con- fidence 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 com- munity showed a mean increase in
8.18 Multimedia Kids 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 equip- ment? A random sample of 250 children between
8.20 Male Teachers Although most school districts do not specifically recruit men to be elementary school teachers, those men who do choose a career in elemen- tary education are highly valued and find the career very rewarding. If there were 40 men in a random sample of 250 elementary school
8.21 Fear Factor In a survey of 1275 Canadians aged 18 and over conducted by EKOS Research, 69% of Canadians said they thought the world is more dan- gerous today than it was 25 years ago.4a. Find a point estimate for the proportion of Canadian adults who fear that the world is more dangerous today
8.22 Mosaic or Melting Pot? The concept of the mosaic where cultural differences within society are deemed valuable and regarded as something that should be preserved-is often used to distinguish Canada from the United States. Based on the online survey of a representative national sample of 1006
8.23 "900" Numbers 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
8.24 Hungry Rats 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
A scientist interested in monitoring chemical contaminants in food, and thereby the accumulation of contaminants in human diets, selected a random sample of n = 50 male adults. It was found that the average daily intake of dairy products was x = 756 grams per day with a standard deviation of s = 35
Construct a 99% confidence interval for the mean daily intake of dairy products for adult men in Example 8.6.
8.25 Find and interpret a 95% confidence interval for a population mean for these values:a. n = 36, 13.1, s = 3.42b. n = 64, x 2.73, s = 0.1047
8.26 Find a 90% confidence interval for a population mean for these values:a. n = 125, x=0.84, s = 0.086b. n 50, x 21.9, s = 3.44e. Interpret the intervals found in parts a and b.
8.27 Find a (1a)100% confidence interval for a population mean for these values: =a. a 0.01, n = 38, x = 34, s = 12b. a 0.10, n = 65, x=1049, s2=51 =c. = 0.05, n = 89, = 66.3, s = 2.48
8.28 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.
8.29 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 8.28?
8.30 A random sample of n measurements is selected from a population with unknown mean and known standard deviation or = 10. Calculate the width of a 95% confidence interval for for these values of n:a. n = 100b. n = 200c. n = 400
8.31 Compare the confidence intervals in Exercise 8.30. What effect does each of these actions have on the width of a confidence interval?a. Double the sample sizeb. Quadruple the sample size
8.32 Refer to Exercise 8.31.a. Calculate the width of a 90% confidence interval for when n = 100.b. Calculate the width of a 99% confidence interval for when n = 100.c. Compare the widths of 90%, 95%, and 99% confi- dence intervals for u. What effect does increasing the confidence coefficient have
8.33 A Chemistry Experiment Due to a variation in laboratory techniques, impurities in materials, and other unknown factors, the results of an experiment in a chemistry laboratory will not always yield the same numerical answer. In an electrolysis experiment, a class measured the amount of copper
8.34 Acid Rain Acid rain, caused by the reaction of certain air pollutants with rainwater, appears to be a growing problem in Eastern Canada. (Acid rain affects the soil and causes corrosion on exposed metal surfaces.) Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure
8.35 'Tweens When it comes to advertising, "tweens" (kids aged 10 to 13) are not ready for the hardline messages that advertisers often use to reach teenagers. One study found that 78% of 'tweens under- stand and enjoy ads that are silly in nature. Unlike teenagers, 'tweens would much rather see
8.36 Ground Beef The meat department of a local supermarket chain packages ground beef using meat trays of two sizes: one designed to hold approxi- mately 0.454 kilograms (kg) of meat, and one that holds approximately 1.36 kg. A random sample of 35 packages in the smaller meat trays produced weight
8.37 Kids Take on Media To provide current and factual information on the role media plays in children's lives, the Canadian Teachers' Federation (CTF) com- missioned Erin Research to conduct definitive research on Canadian children's experience with communica- tions media. The research involved
8.38 SUVs A sample survey is designed to estimate the proportion of sports utility vehicles being driven in PEI. A random sample of 500 registrations are selected from a PEI database, and 68 are classified as sports utility vehicles.a. Use a 95% confidence interval to estimate the pro- portion of
8.39 e-Shopping In a report of why e-shoppers aban- don their online sales transactions, Alison Stein Well- ner found that "pages took too long to load" and "site was so confusing that I couldn't find the product" were the two complaints heard most often. Based on custom- ers' responses, the
8.40 What's Normal? 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 Edu- cation, had a mean of 36.81 Celsius and a standard deviation of 0.73.a. Construct a 99% confidence interval
8.41 Multiculturalism? Based on the online survey of a representative national sample of 1006 Canadian adults, conducted by Angus Reid, 55% think multicul- turalism has been "very good" or "good" for Canada. Further, the survey found 54% want Canada to be a melting pot where immigrants assimilate
8.42 A Tolerant Society? Refer to Exercise 8.41. Respondents across the country were asked whether Canada is tolerant or intolerant toward nine different minority groups. One-third of respondents (33%) think Canadian society is intolerant toward Muslims, 30% say it is intolerant toward Aboriginal
8.43 Voter Turnout in Canada How likely are you to vote in the next federal general election? A random sample of 300 adults was taken, and 192 of them said. that they always vote in federal general elections.a. Construct a 95% confidence interval for the propor- tion of adult Canadians who say they
The wearing qualities of two types of automobile tires were compared by road-testing samples of n = n = 100 tires for each type. The number of kilometres until wearout was defined as a specific amount of tire wear. The test results are given in Table 8.4. Esti- mate (u), the difference in mean
The scientist in Example 8.6 wondered whether there was a difference in the average daily intakes of dairy products between men and women. He took a sample of n = 50 adult women and recorded their daily intakes of dairy products in grams per day. He did the same for adult men. A summary of his
8.44 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 (12).b. Based on the confidence interval in parta, can you conclude that there is a
8.46 Independent random samples of size n = n 100 were selected from each of two populations. The mean and standard deviations for the two samples were x=125.2, x = 123.7, s = 5.6, and $2 = 6.8.a. Construct a 99% confidence interval for estimating the difference in the two population means.b. Does
8.47 Independent random samples of size n = n = 500 were selected from each of two populations. The mean and standard deviations for the two samples were x=125.2, x2=123.7, s = 5.6, and s = 6.8.a. Find a point estimate for the difference in the two population means. Calculate the margin of error.b.
8.48 Selenium A small amount of the trace element selenium, 50-200 micrograms (jug) per day, is con- sidered essential to good health. Suppose that random samples of n = n2 = 30 adults were selected from two regions of Canada and that a day's intake of selenium, from both liquids and solids, was
8.50 Teaching Biology In developing a standard for assessing the teaching of precollege sciences in the United States, an experiment was conducted to evaluate a teacher-developed curriculum, "Biology: A Community Context" (BACC) that was standards- based, activity-oriented, and inquiry-centred.
8.51 Are You Dieting? An experiment was con- ducted to compare two diets A and B designed for weight reduction. Two groups of 30 overweight dieters each were randomly selected. One group was placed on diet A and the other on diet B, and their weight losses were recorded over a 90-day period. The
8.52 Starting Salaries In an attempt to compare the starting salaries of university graduates majoring in education and social sciences, random samples of 50 recent university graduates in each major were selected and the following information was obtained:a. Find a point estimate for the
8.53 Biology Skills Refer to Exercise 8.50. In addi- tion 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
8.54 Hotel Costs Refer to Exercise 8.19. 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
8.55 Noise and Stress 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
8.56 What's Normal II Of the 130 people in Exercise 8.40, 65 were female and 65 were male.15 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,
A bond proposal for school construction will be submitted to the voters at the next municipal election. A major portion of the money derived from this bond issue will be used to build schools in a rapidly developing section of the city, and the remainder will be used to renovate and update school
8.60 M&Ms Does the maker of M&Ms(Mars, Inc.) use the same proportion of red candies in its plain and peanut varieties? A random sample of 56 plain M&Ms contained 12 red candies, and another random sample of 32 peanut M&Ms contained 8 red candies.a. Construct a 95% confidence interval for the
8.61 Welfare Issue The National Post reported in April 2005 that long-term welfare recipients in Ontario would receive individual coaching until they found jobs. According to the article, the provincial govern- ment would hire a private firm to get welfare recipients back into the workforce.
8.62 Consumer Outlook According to the 14th Annual RBC Homeownership Survey conducted by Ipsos-Reid in 2007, most Canadians continued to think purchasing a home was a good investment. 17 Addition- ally, there was less concern about interest and/or mort- gage rate hikes than at the same time the
8.63 Consumer Outlook, continued Refer to Exercise 8.60. In a 2007 opinion poll, suppose that 430 adults identified those who thought mortgage rates would go up. The following question was posed: Do you think Bank of Canada may start hiking the base rate in coming years? Suppose that 390 who
8.64 Catching a Cold Do well-rounded people get fewer colds? A study in the Chronicle of Higher Edu- cation was conducted by scientists at Carnegie Mellon University, the University of Pittsburgh, and the Uni- versity of Virginia. They found that people who have only a few social outlets get more
8.65 Union, Yes! A sampling of political candi- dates-200 randomly chosen from the West and 200 from the East was classified according to whether the candidate received backing by a national labour union and whether the candidate won. In the West, 120 win- ners had union backing, and in the East,
8.66 Birth Order and University Success In a study of the relationship between birth order and university success, an investigator found that 126 in a sample of 180 university graduates were firstborn or only children. In a sample of 100 non-graduates of comparable age and socioeconomic background,
8.67 Ads in Outer Space? Do you think that we should let The Source film a commercial in outer space? The commercialism of our space program is a topic of great interest since Dennis Tito paid $20 mil- lion dollars to ride along with the Russians on the space shuttle. In a survey of 500 men and 500
8.68 Generation Next Born between 1980 and 1990, Generation Next is engaged with technology, and the vast majority is dependent upon it.20 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
8.69 Excedrin or Tylenol? In a study to compare the effects of two pain relievers, it was found that of n = 200 randomly selected individuals instructed to use the first pain reliever, 93% indicated that it relieved their pain. Of n 450 randomly selected individuals instructed to use the second
8.70 Auto Accidents 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
A corporation plans to issue some short-term notes and is hoping that the interest it will have to pay will not exceed 11.5%. To obtain some information about this problem, the corporation marketed 40 notes, one through each of 40 brokerage firms. The mean and standard deviation for the 40 interest
Producers of polyvinyl plastic pipe want to have a supply of pipes sufficient to meet marketing needs. They wish to survey wholesalers who buy polyvinyl pipe in order to estimate the proportion who plan to increase their purchases next year. What sample size is required if they want their estimate
A personnel director wishes to compare the effectiveness of two methods of training industrial employees to perform a certain assembly operation. A number of employees are to be divided into two equal groups: the first receiving training method 1 and the second training method 2. Each will perform
8.71 Find a 90% one-sided upper confidence bound for the population mean for these values:a. n = 40, s2 = 65, x = 75b. n =100, s =2.3, x=1.6
8.72 Find a 99% lower confidence bound for the binomial proportion p when a random sample of n=400 trials produced x = 196 successes.
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