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mathematics
statistics

Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions

This section presented Formulas 6-5 and 6-6, which are used for determining sample size. In both cases we assumed that the population is infinite or very large, or that we are sampling with replacement. When we have a relatively small population with size N and sample without replacement, we modify
Assume that a sample is used to estimate a population proportion p. Find the margin of error that corresponds to the given values of n and x and the degree of confidence.n = 4275, x = 2576, 98%
Consider the following statement: "The results from this poll differ, 19 times out of 20, by no more than 1 percentage point in either direction from the results that would be obtained by surveying all voters in Canada." Find the sample size suggested by this statement.
A newspaper article indicates that an estimate of the unemployment rate involves a survey of 47,000 people. If the reported unemployment rate must have an error no larger than 0.2 percentage points and the rate is known to be about 8%, find the corresponding confidence level.
Heights of female students are normally distributed with a mean of 64.2 in and a standard deviation of 2.6 in. How many female students must be surveyed if we want to estimate the percentage who are taller than 5 ft? Assume that we want 98%.confidence that the error is no more than 2.5 percentage
A one-sided confidence interval for p can be written as p < + E or p > - E, where the margin of error E is modified by replacing zα/2 with zα. If Air Borealis wants to report an on-time performance of at least x percent with 95% confidence, construct the appropriate one-sided confidence
Special tables are available for finding confidence intervals for proportions involving small numbers of cases where the normal distribution approximation cannot be used. For example, given three successes among eight trials, the 95% confidence interval found in Standard Probability and Statistics
Assume that a sample is used to estimate a population proportion p. Find the margin of error that corresponds to the given values of n and x and the degree of confidence.n = 887, x = 209, 90%
Use the given sample data and degree of confidence to construct the interval estimate of the population proportion p.n = 800, x = 600, 95% confidence
Use the given sample data and degree of confidence to construct the interval estimate of the population proportion p.n = 2000, x = 300, 99% confidence
Use the given sample data and degree of confidence to construct the interval estimate of the population proportion p.n = 2475, x = 992, 90% confidence
Use the given sample data and degree of confidence to construct the interval estimate of the population proportion p.n = 5200, x = 1024, 98% confidence
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.Margin of error: 0.02; confidence level: 95%; and unknown
Suppose that a sample of customers per hour were randomly taken from a store and that the sample standard deviation of the number of customers per hour was 2.4 are based on this information. Assume that the number of customers per hour is normally distributed. If the sample size were 15 instead of
Suppose that a sample of customers per hour were randomly taken from a store and that the sample standard deviation of the number of customers per hour was 2.4 are based on this information. Assume that the number of customers per hour is normally distributed. If the level of confidence were 99%
Suppose that a sample of customers per hour were randomly taken from a store and that the sample standard deviation of the number of customers per hour was 2.4 are based on this information. Assume that the number of customers per hour is normally distributed. Would a 99% confidence interval with a
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.A container of car antifreeze is supposed to hold 3785 mL of the liquid. Realizing that fluctuations are inevitable, the quality control manager wants to be quite sure that the standard
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. Refer to Data Set 21 in Appendix B. a. Use the range rule of thumb (see Section 2-5) to estimate σ, the standard deviation of values for the "depth" of high-price diamonds. b. Use the
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. A sample of 35 skulls is obtained for Egyptian males who lived around 1850 BCE. The maximum breadth of each skull is measured with the result that = 134.5 mm and s = 3.5 mm (based on data
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. A sample consists of 75 TV sets purchased several years ago. The replacement times of those TV sets have a mean of 8.2 years and a standard deviation of 1.1 years (based on data from
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. The listed values are waiting times (in minutes) of customers at the Humber Valley Credit Union, where customers enter a single waiting line that feeds three windows. Construct a 95%
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. Off-season football players often participate in community events and charity fundraisers. Suppose a firm is bidding to provide T-shirts for players who are representing the CFL in such
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution. Refer to Data Set 4 in Appendix B. a. Use the range rule of thumb (see Section 2-5) to estimate s, the standard deviation of the annual snowfall (in centimetres) of the first 31 cities
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.Refer to Data Set 11 in Appendix B.a. Use the range rule of thumb (see Section 2-5) to estimate s, the standard deviation of the weights of brown M&M plain candies.b. Construct a 98%
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.A journal article includes a graph showing that sample data are normally distributed.a. The degree of confidence is inadvertently omitted when this confidence interval is given: 2.8 < σ
Assume that each sample is obtained by randomly selecting values from a population with a normal distribution.In constructing confidence intervals for Ïƒ or Ïƒ2, we use Table A-4 to find the critical values x2L and x2R, that table applies only to cases in which n ‰¤
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that the population has a normal distribution. Heights of female students: 95% confidence; n = 10, = 64.2 in, s = 2.6 in
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that the population has a normal distribution. Grade-point averages: 99% confidence; n = 15, = 2.76, s = 0.88
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that the population has a normal distribution. Test scores: 90% confidence; n = 16, = 77.6, s = 14.2
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. In each case, assume that the population has a normal distribution. Cost of basic phone service: 95% confidence; n = 19, = $15.30, s = $1.25
Suppose that a sample of customers per hour were randomly taken from a store and that the sample standard deviation of the number of customers per hour was 2.4 are based on this information. Assume that the number of customers per hour is normally distributed. Construct a 95% confidence interval of
A human resources specialist has compiled annual numbers of person-days of work lost, due to work stoppages, in the water-based transportation industry. These are the results (based on data from Human Resources Canada, Workplace Information Directorate): n = 40 = 38,015.7 median = 18,240.0 s =
In a Roper survey of 1998 randomly selected adults, 24% included loud commercials among the annoying aspects of television. Construct the 99% confidence interval for the percentage of all adults who are annoyed by loud commercials.
You have just been hired by General Motors to tour Canada giving randomly selected drivers test rides in a new Corvette (yeah, right). After giving the test drive, you must ask the rider whether he or she would consider buying a Corvette. How many riders must you survey to be 97% confident that the
An auto parts supplier wants information about how long car owners plan to keep their cars. A random sample of 25 car owners results in = 7.01 years and s = 3.74 years, respectively (based on data from a Roper poll). Assuming that the sample is drawn from a normally distributed population, find a
Using the same sample data from Exercise 3, find a 95% confidence interval for the population standard deviation.
The Angus Reid Group randomly selected 1000 Ontario residents ages 18 and older by phone. Fifty-four percent of those surveyed believe the private sector should be responsible for ensuring there are jobs for Ontario residents. Construct the 95% confidence interval for the true proportion of Ontario
In a Gallup poll of 1004 adults, 93% indicated that restaurants and bars should refuse service to patrons who have had too much to drink. If you plan to conduct a new poll to confirm that the percentage continues to be correct, how many randomly selected adults must you survey if you want 98%
In designing a new machine to be used on an assembly line at a General Motors plant, an engineer obtains measurements of arm-lengths of a random sample of male machine operators. The following values (in centimetres) are obtained. Construct the 95% confidence interval for the mean arm length of all
Verbal PSAT scores of a random sample of 40 college-bound high-school juniors have a mean of 40.7, a standard deviation of 10.2, and a distribution that is normal (based on data from Educational Testing Service). Find a 99% confidence interval estimate of the population mean.
A company that produces electronic ignition systems for an engine developer wants to select a suitable sample size for monitoring the mean defect-free life of the ignition systems. The company wants to be 95% confident that the true mean life of these systems will be estimated within 6300 hours. A
The college statistics club is reviewing its order for sweat suits for the new fall semester. Its review involves the random sample of heights for 24 students, listed here (in inches):Find each of the following: a. mean b. median c. mode d. midrange e. range f. variance g. standard deviation h.
A genetics expert has determined that for certain couples, there is a 0.25 probability that any child will have an X-linked recessive disorder. a. Find the probability that among 200 such children, at least 65 have the X-linked recessive disorder. b. A subsequent study of 200 actual births reveals
Claim: A coin is fair. Then the coin turns up heads 27 times in 30 tosses. What do you conclude? (Do not use formal procedures and exact calculations. Use only the rare event rule described in Section 7-1, and make subjective estimates to determine whether events are likely.)
In explaining the need to attract new business, Antigonish and Guysborough counties claim that, for women, the mean income in that region is $14,000. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about a proportion, and σ for a
The Canadian Automobile Association warns that motorists are being seduced by ads to buy higher octane gas than is useful. Test the claim that fewer than 10% of cars on the road have a design that benefits from higher octane gasoline. Assume that a hypothesis test of the given claim will be
The buyer for a hospital supply company recommends not buying the new digital thermometers because they vary more than the old thermometers with a standard deviation of 0.33°C. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about
Left-tailed test; α = 0.05 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Left-tailed test; α = 0.01 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Two-tailed test; α = 0.01 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Two-tailed test; α = 0.10 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Right-tailed test; α = 0.025 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Left-tailed test; α = 0.025 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
Claim: A die is fair. Then the die turns up a 1 nine times in 60 rolls. What do you conclude? (Do not use formal procedures and exact calculations. Use only the rare event rule described in Section 7-1, and make subjective estimates to determine whether events are likely.)
Two-tailed test; α = 0.02 Find the critical z values for the given conditions. In each case assume that the normal distribution applies, so Table A-2 can be used. Also, draw a graph showing the critical value and critical region.
From a study of consumer buying: The claim is µ = 0.21, and the sample statistics include n = 32, = 0.83, and s = 0.24. Find the value of the test statistic z.
From an article on the ages of humans: The claim is µ = 73.4, and the sample statistics include n = 35, = 69.5, and s = 8.7.Find the value of the test statistic z.
From research on seatbelt use: The claim is µ < 1.39, and the sample statistics include n = 123, = 0.83, and s = 0.16. Find the value of the test statistic z.
From a study of the amounts of Moosehead Beer in cans: The claim is µ = 355, and the sample statistics include n = 36, = 360.6, and s = 3.3. Find the value of the test statistic z.
Someone suggests that in testing hypotheses, you can eliminate a type I error by making α = 0. In a two-tailed test, what critical values correspond to α = 0? If α = 0, will the null hypothesis ever be rejected?
Claim: Women who eat blue M&M candies have a better chance of having a baby boy. Then 50 such women give birth to 27 boys and 23 girls. What do you conclude? (Do not use formal procedures and exact calculations. Use only the rare event rule described in Section 7-1, and make subjective estimates to
Claim: A roulette wheel is fair. Then the number 7 occurs seven times in seven trials. (A fair roulette wheel has 38 equally likely slots, one of which is a 7.) What do you conclude? (Do not use formal procedures and exact calculations. Use only the rare event rule described in Section 7-1, and
Health Canada claims that a pharmaceutical company makes cold caplets that contain amounts of acetaminophen with a mean different from the 650 mg amount indicated on the label. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about a
The college registrar claims that the times students require to earn a college diploma have a mean less than 5 years. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about a proportion, and σ for a claim about variation. a. Express
The Conservative Party M.P. claims that she is currently favored by more than half of all voters in her riding. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about a proportion, and σ for a claim about variation. a. Express the
The Home Electronics Supply Company claims that its home circuit breakers trip at levels that have less variation than circuit breakers made by its major competitor, which has variation described by σ = 0.4 amp. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim
Statistics Canada claims that over 2% of all adults are enrolled in school full time. Assume that a hypothesis test of the given claim will be conducted. Use µ for a claim about a mean, p for a claim about a proportion, and σ for a claim about variation. a. Express the claim in everyday
Test the claim that the population mean µ = 75, given a sample of n = 100 for which = 78 and s = 15. Test at the α = 0.05 significance level.
An ambitious young worker claims that older employees have a better chance of being CEOs than younger employees. To confirm this, he sampled the ages of CEOs for 31 companies. The mean age in the sample was found to be 41.77, with a standard deviation of 10.24 (based on data from Profit, May 29,
The yearly rates of traffic accidents and violations were studied for a group of 137 young adult males who volunteered for treatment for substance abuse. For the five years before receiving treatment, their mean accident rate was 0.123 with a standard deviation of 0.167 (based on data from "Does
In a study of distances travelled by buses before the first major engine failure, a sampling of 191 buses resulted in a mean of 154,700 km and a standard deviation of 60,000 km. At the 0.05 level of significance, test the manufacturer's claim that mean distance travelled before a major engine
A poll of 100 randomly selected car owners revealed that the mean length of time that they plan to keep their cars is 7.01 years and the standard deviation is 3.74 years (based on data from a Roper poll). The president of the Kamloops Car Park is trying to plan a sales campaign targeted at car
When 200 convicted embezzlers were randomly selected, the mean length of prison sentence was found to be 22.1 months and the standard deviation was found to be 8.6 months. Kim Patterson is running for political office on a platform of tougher treatment of convicted criminals. Test her claim that
A nighttime cold medicine bears a label indicating the presence of 600 mg of acetaminophen in each fluid oz of the drug. Suppose that Health Canada randomly selected 65 one-oz samples and found that the mean acetaminophen content was 589 mg, and the standard deviation was 21 mg. Using α = 0.01,
An insurance company is reviewing the driving habits of women aged 16-24 to determine whether they should pay higher premiums than women in a higher age bracket. In a study of 750 randomly selected women drivers aged 16-24, the mean driving distance for one year is 9750 km and the standard
A fish-processing company is concerned about the shelf life of its new cat food. A quality manager claims that the mean product shelf life of cans from the Dartmouth facility is less than the advertised mean (of 12 months) for its product's shelf life. Test that claim using the 0.005 level of
The true value of one type of degree or diploma cannot be quantitatively measured, but we can measure its relative impact on starting salary. Graduates from Quebec universities with a B.A. or a B.Sc. degree have a mean annual starting salary of $28,300. Sixty-five Quebec graduates with a civil
The mean time between failures (in hours) for a Telektronic Company radio used in light aircraft is 420 h. After 35 new radios were modified in an attempt to improve reliability, tests showed that the mean time between failures for this sample is 385 h and the standard deviation is 24 h. Use a 0.05
Test the claim that µ > 750, given a sample of n = 36 for which = 800 and s =100. Use a significance level of α = 0.01.
An investment advisor is trying to persuade an investor to switch from her current fund holdings, claiming that the advisor's portfolio recommendations have had a greater one-year return rate than the investor's current funds. Last year, the investor's annual return rate was 35%. Use a 0.01 level
Refer to Data Set 1 in Appendix B for the total weights of garbage discarded by households in one week. For that data set, the mean is 27.44 lb and the standard deviation is 12.46 lb. At the 0.01 level of significance, test the claim that the mean weight of all garbage discarded by households each
If we refer to the weights (in grams) of quarters listed in Data Set 13 in Appendix B, we find 50 weights with a mean of 5.622 g and a standard deviation of 0.068 g. Use a 0.01 significance level to test the claim that the mean weight of quarters in circulation is 5.670 g. If the claim is rejected,
Analysis of the last digits in data sometimes reveals whether the data have been accurately measured and reported. If the last digits are uniformly distributed from 0 to 9, then their mean should be 4.5. The last digits in the published numbers of sitting days for federal Parliaments are used to
A package of M&M plain candies is labeled as containing 1361 g, and there are 1498 candies, so the mean weight of the individual candies should be 1361/1498, or 0.9085 g. In a test to determine whether consumers are being cheated, a sample of 33 brown M&Ms is randomly selected. (See Data
A journal article reported that a null hypothesis of µ = 100 was rejected because the P-value was less than 0.01. The sample size was given as 62, and the sample mean was given as 103.6. Find the largest possible standard deviation.
In Exercise 17, find the largest sample mean below 12 months that will support the claim that the mean is less than 12 months. (Use the same sample size and sample standard deviation.)
Suppose you are given these hypotheses: H0: µ ≤ 25, H1: µ > 25; and that the standard deviation from a sample of 100 is 2.4. What is the power of the test at a 5% level of significance if the alternative mean is 25.2?
Which would increase the power in Exercise 27 by more: increasing the alternative mean to 25.5 and keeping α = 0.05 or keeping the alternative mean at 25.2 and increasing α to 0.1?
For the power calculation in Exercise 27, what would the alternative mean need to be at a 5% level of significance if we want the power to be at least 95%?
Test the claim that µ < 2.50, given a sample of n = 64 for which = 2.45 and s = 0.80. Use a significance level of α = 0.02.
In a certain accounting office, workers have been processing 60 tax returns per day on average with a standard deviation of 10.2. The office introduced a new protocol in order to see if there would be any significant change in the average number of returns processed per day. For a random sample of
One of the characteristics of the power of the test is that, for the same alternative mean, the power is greater for the appropriate one-tailed test than for the two-tailed test. Suppose we have the same situation as in Exercise 30 but the alternative hypothesis is H1: µ < 60. Compared to the
In some disciplines, both the level of significance and the power are taken into consideration in calculating the sample size. Suppose we have the hypotheses: H0: µ < 50, H1: µ > 50 and that based on prior information, the standard deviation is 8.5. If we test at a 5% level of significance
Test the claim that a population mean is different from 32.0, given a sample of n = 75 for which = 31.8 and s = 0.85. Use a significance level of α = 0.01.
In April 1994, during a spring of unusually good hitting in professional baseball, a columnist for the Toronto Star hinted at a "conspiracy" by managers in which they "juiced" the baseballs to increase excitement in the game. Suppose that tests of the old balls showed that when dropped 24 ft onto a
The Mackenzie Valley Bottling Company distributes root beer in bottles labeled 32 oz. An inspector randomly selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.8 oz and a sample standard deviation of 0.75 oz. Using a 0.01 significance level, test the inspector's
In a study of consumer habits, researchers designed a questionnaire to identify compulsive buyers. For a sample of consumers who identified themselves as compulsive buyers, questionnaire scores have a mean of 0.83 and a standard deviation of 0.24. Assume that the subjects were randomly selected and
Planners in Ontario's Durham region compiled data for the value of building permits. The mean for all building permits (in thousands of dollars) was 97. But for a random sample of 38 permits in the smaller Durham region communities of Scugog, Brock, Clarington, and Uxbridge, the mean value was
Your investment goal is to choose only from mutual fund groups with at least 10% foreign equity. To determine whether the Canadian equity funds group meets your criterion, you randomly sample 33 of the funds in that category. The mean foreign equity percentage in your sample is 8.386, with a
a. H0: µ = 37.0 n = 7 α = 0.05 b. H0: µ ≥ 100 n = 12 α = 0.05 c. H1: µ > 32 n = 9 α = 0.01 Find the critical t values for the given hypotheses, sample sizes, and significance levels.

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