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statistics

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

Refer to Data Set 2 in Appendix B. In two separate analyses, use the data in the two columns labeled "Supine." Both columns represent the temperatures of 11 subjects after they lay face up for a period of time. (In the first experiment, the subjects sat first, before lying down; in the second
For each of 12 organizations, the cost of operation per client was found. The 12 scores have a mean of $2133 and a standard deviation of $345. At the 0.01 significance level, test the claim of a stockholder who complains that the mean for all such organizations exceeds $1800 per client.Use the
The skid properties of a snow tire have been tested, and a mean skid distance of 47 m has been established for standardized conditions. A new, more expensive tire is developed, but tests on a sample of 17 new tires yield a mean skid distance of 45 m with a standard deviation of 3.7 m. Because of
A major bank is concerned about the amount of debt being accrued by customers using its credit cards. The Board of Directors voted to institute an expensive monitoring system if the mean for all of the bank's customers is greater than $2000. The bank randomly selected 50 credit-card holders and
When a poultry farmer uses her regular feed, the chickens attain normally distributed weights with a mean of 1.77 kg. In an experiment with an enriched feed mixture, nine chickens are born that attain the weights (in kg) given below.a. Use a 0.01 significance level to test the claim that the mean
In a study of factors affecting hypnotism, visual analogue scale (VAS) sensory ratings were obtained for 16 subjects. For these sample ratings, the mean is 8.33 while the standard deviation is 1.96. At the 0.01 level of significance, test the claim that this sample comes from a population with a
A critic of Canada Post claims that its financial returns are typically $200 million less than forecast. In five of the years of the 1990s, the mean difference (in millions of dollars) between Canada Post's forecast and actual financial positions was 218.8, with a standard deviation of 118.76
Because of a merger, a Vancouver executive will commute regularly to San Francisco for important meetings. To plan for travel time, she has compiled, as shown, a sample of flight times, in hours, for flights from Vancouver to San Francisco (based on data from Gary Murphy, chief flight dispatcher,
A Calgary observatory records daily the mean counting rates for cosmic rays for that specific day (data from the National Geophysical Data Center). These recorded values are approximately normally distributed. If, for a randomly selected sample of the observatory's records, = 3455, and s = 126.7,
Using the weights of only the blue M&Ms listed in Data Set 11 of Appendix B, test the claim that the mean is at least 0.9085 g, the mean value necessary for the 1498 M&Ms to produce a total of 1361 g as the package indicates. Use a 0.05 significance level. For the blue M&Ms, = 0.9014
a. H0: µ ≤ 1.07 n = 7 α = 0.01 b. H1: µ > 75.2 n = 14 α = 0.05 c. H1: µ ≠ 64 n = 10 α = 0.10 Find the critical t values for the given hypotheses, sample sizes, and significance levels.
Using the weights of only the brown M&Ms listed in Data Set 11 of Appendix B, test the claim that the mean is greater than 0.9085 g, the mean value necessary for the 1498 M&Ms to produce a total of 1361 g as the package indicates. Use a 0.05 significance level. For the brown M&Ms, =
Listed here are the total electric energy consumption amounts (in kWh) for the home of a statistics professor during seven different years:The utility company claims that the mean annual consumption amount is 11,000 kWh and offers a budget payment plan based on that amount. At the 0.05 significance
Given here are the birth weights (in kilograms) of male babies born to mothers on a special vitamin supplement. At the 0.05 level of significance, test the claim that the mean birth weight for all male babies of mothers given vitamins is equal to 3.39 kg, which is the mean for the population of all
Rita Gibbons is a stand-up comedian who videotapes her performances and records the total of the times she must wait for audience laughter to subside. Given here are the times (in seconds) for 15 different shows in which she used a new routine. Test the claim that the mean time is greater than 63.2
An umbrella salesperson has moved her base from Winnipeg to Atlantic Canada. Believing that the mean annual precipitation for communities in Atlantic Canada is over twice the annual amount in Winnipeg (526 mm), she expects to do a great business. Refer to the top eight entries for annual
Because of certain conditions, a hypothesis test requires the Student t distribution, as described in this section. Assume that the standard normal distribution was incorrectly used instead. Does using the standard normal distribution make you more or less likely to reject the null hypothesis, or
When finding critical values, we sometimes need significance levels other than those available in Table A-3. Some computer programs approximate critical t values bywheredf = n - 1e = 2.718and z is the critical z score. Use this approximation to find the critical t score corresponding to n = 10 and
Refer to the data in Exercise 23 and assume that you're testing the claim that µ > 63.2 s. Find β (the probability of a type II error), given that the actual value of the population mean is µ = 72.1 s.
Use a significance level of α = 0.05 to test the claim that µ ≠ 64.8. The sample data consist of 12 scores for which = 59.8 and s = 8.7.Assume that the sample is randomly selected from a population with a normal distribution. Test the given claim by using the traditional method of testing
Use a significance level of α = 0.01 to test the claim that µ < 927. The sample data consist of 10 scores for which = 874 and s = 57.3.Assume that the sample is randomly selected from a population with a normal distribution. Test the given claim by using the traditional method of testing
A student used just one trade publication to price desktops that have at least a 20 GB hard drive and a 700 MHz processor speed. To justify relying on the one source, he took a sample of prices for such systems, as quoted in dealers' ads in the publication. Assume the industry mean price for such a
Refer to the display in Exercise 5. If the claim is changed from "is no different from the industry average" to "is greater than the industry average," how are the values in the right column of the table affected?
The top ten punt returners in CIAU football have a mean for total-yards-returned in the season of 377 yards (based on data from the CIAU Football website). To support his arguments for a pay raise, a scout claims that punt returners he has recruited have performed better than the mean for top
The expense of moving the storage yard for the Consolidated Package Delivery Service (CPDS) is justified only if it can be shown that the daily mean travel distance will be less than 342 km. In trial runs of 12 delivery trucks, the mean and standard deviation are found to be 318 km and 67 km,
Data Set 2 in Appendix B is derived from research into the effects of cold and other factors on human body temperature. Use just the data in the leftmost column, representing the temperatures of 11 subjects after they sat perfectly still for a period of time. Test the claim that the mean body
In a study of store checkout scanners, 1234 items were checked and 20 of them were found to be overcharges. Use a 0.05 level of significance to test the claim that with scanners, 1% of sales are overcharges. (Before scanners were used, the overcharge rate was estimated to be about 1%) Based on
"Bystanders perform CPR correctly less than half the time," according to a newspaper article that noted that among 662 cases in which bystanders gave CPR, 46% performed the CPR correctly. Use a 0.025 significance level to test the article's claim.Test the given claim, and draw the appropriate
Auto insurance companies are beginning to consider raising rates for those who use cell phones while driving. A consumer group claims that the problem really isn't too serious because only 10% of drivers use cell phones. The insurance industry conducts a study and finds that among 500 randomly
Many researchers consider that a 75% response rate to a survey is quite good. In spring 1998, Statistics Canada surveyed thousands of representatives of businesses, governments, and institutions regarding their capital spending plans. At the same time, they wished to study the response rates. Of
In clinical studies of the allergy drug Seldane, 70 of the 781 subjects experienced drowsiness (based on data from Merrell Dow Pharmaceuticals, Inc.). A competitor claims that 8% of Seldane users experience drowsiness. Use a 0.10 significance level to test that claim.Test the given claim, and draw
Late in the campaign for the June 1997 federal election, the Angus Reid Group conducted an opinion poll of public preferences. The poll found the Liberals had the support of 42% of the 3208 voters surveyed. In the election, the Liberals won 38.4% of the popular vote (based on reports by Reuters
Dr. Kelly Roberts is dean of a medical school and must plan courses for incoming students. The college president is encouraging her to increase the emphasis on pediatrics, but Dr. Roberts argues that fewer than 10% of medical students prefer pediatrics. She refers to sample data indicating that 64
Several dentist offices were concerned with their 8% rate of no-shows for appointments. The Canadian Dental Association recommended that to reduce these no-shows, the receptionist should call each patient a day before his or her scheduled appointment, as a reminder and confirmation. A study was
In one study of 71 smokers who tried to quit smoking with nicotine patch therapy, 32 were not smoking one year after the treatment. Use a 0.10 level of significance to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.
In a study of the risks to children of automobile accidents, 400 records were randomly selected for the ages of children who died as occupants in motor vehicles. Of these, 285 were teenagers from 15 to 19 years old (based on data from Health Canada). At the 0.03 level of significance, test the
A research poll of 1012 adults showed that among those who used fruitcakes, 28% ate them and 72% used them for other purposes, such as doorstops, birdfeed, and landfill. This surprised fruitcake producers, who believe that a fruitcake is an appealing food. The president of the Tombits Food Company
Environmental concerns often conflict with modern technology, as is the case with birds that pose a hazard to aircraft during takeoff. An environmental group states that incidents of bird strikes are too rare to justify killing the birds. A pilots' group claims that among aborted takeoffs leading
A Prevention magazine article reported on a poll of 1257 adults. The article noted that among those polled, 27% smoke, and 82% of those who smoke have tried to stop at least once. How many of the surveyed people are smokers who have tried to stop at least once? At the 0.05 significance level, test
In a study of the prevalence of cold/flu symptoms in December 2000, 44 residents of Ottawa are tested in December, and five of them have the symptoms (based on data from The Globe and Mail, December 20, 2000). We want to use a 0.01 significance level to test the claim that the percentage of
Chemco, a supplier of chemical waste containers, finds that 3% of a sample of 500 units are defective. Being fundamentally dishonest, the Chemco production manager wants to make a claim that the rate of defective units is no more than some specified percentage, and he doesn't want that claim
Refer to Exercise 9. If the true value of p is 0.45, find β, the probability of a type II error.
The quality control manager at the Telektronic Company considers production of telephone-answering machines to be "out of control" when the overall rate of defects exceeds 4%. Testing of a random sample of 150 machines revealed that nine are defective, so the sample percentage of defects is 6%. The
In a recent year, 64% of all formal complaints to government institutions were resolved. The other complaints were unresolved, discontinued, or not substantiated. A spokesperson for Revenue Canada claims that they had a more positive record. In a sample of 58 complaints received, 42 were resolved
Ralph Carter is a high-school history teacher who says that if students are not aware of the Holocaust, then the curriculum should be revised to correct that deficiency. A Roper survey of 506 high-school students showed that 268 of them did not know that the term "Holocaust" refers to the Nazi
Refer to Data Set 8 in Appendix B and consider only those statistics students who are 21 or older. Find the sample percentage of smokers in that age group, then test the claim that statistics students aged 21 or over smoke at a rate that is less than 32%, which is the smoking rate for the general
In past years, the percentage of civilian medical doctors leaving Canada who are from Saskatchewan has been equal to 5.4%. In a more recent sample of 120 civilian doctors leaving Canada, 10 were from Saskatchewan (based on data from the Southam Medical Database). At the 0.05 level of significance,
A mutual funds specialist claims that two-year return rates are greater than one-year return rates for 35% of funds on the market. Test that claim using a 0.05 significance level. For sample data, refer to Data Set 10 of Appendix B.Test the given claim, and draw the appropriate graph. Use the
Based on seven years of data collected by Transport Canada, 45.8% of all bird strikes on moving aircraft involve gulls. Suppose that the next year, planes are asked to emit gull-repelling sound effects, and that of 364 bird-strike incidents, 150 involve gulls. Test the claim that the sound effects
a. H0: σ = 15n = 10α = 0.01b. H1: σ > 0.62n = 27α = 0.01c. H1: σ < 14.4n = 21α = 0.05Use Table A-4 to find the critical values of x2 based on the given information.
For randomly selected adults, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 24 randomly selected college professors resulted in IQ scores having a standard deviation of 10. A psychologist is quite sure that college professors have IQ scores that
Systolic blood pressure results from contraction of the heart. In comparing systolic blood pressure levels of men and women, Dr. Jane Taylor obtained readings for a random sample of 50 women. The sample mean and standard deviation were found to be 130.7 and 23.4, respectively. If systolic blood
A study examined the effects of a stay in the Arctic on a person's tolerance for cold. After a stay in the Arctic, three subjects were exposed to cold in experimental conditions and the effects noted. The subjects' mean skin temperatures had a standard deviation of 2.11°C after their exposure to
Based on data from a health survey, men aged 25-34 have heights with a standard deviation of 2.9 in. Test the claim that men aged 45-54 have heights with a different standard deviation. The heights of 25 randomly selected men in the 45-54 age bracket are_ listed below.Use the traditional method to
An investor claims that the variability between the two-year return rates of different mutual funds is greater than when she began investing. Refer to the two-year return column in Data Set 10 in Appendix B. If the two-year return rates for different funds had a standard deviation of 10.11 when
Use Table A-4 to find the range of possible P-values in the given exercises, a. Exercise 3 b. Exercise 5 c. Exercise 9
For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value, found in Table A-2. For example, if we want to approximate the two critical values of x2 in a two-tailed hypothesis test with
Repeat Exercise 16 using this approximation (with k and z as described in Exercise 16):
Refer to Exercise 5. Assuming that s is actually 4.0, find β (the probability of a type II error). See Exercise 27 from Section 7-3 and modify the procedure so that it applies to a hypothesis test involving a instead of µ.
When using the hypothesis testing procedure of this section, will the result be dramatically affected by the presence of an outlier? Describe how you arrived at your response.
a. H1: σ < 1.22 n = 23 α = 0.025 b. H1: σ > 92.5 n = 12 α = 0.10 c. H0: σ < 0.237 n = 16 α = 0.05 Use Table A-4 to find the critical values of x2 based on the given information.
The last digits of sample data are sometimes used in an attempt to determine whether the data have been measured or simply reported by the subject. Reported data often have last digits with disproportionately more 0's and 5's. Measured data tend to have last digits with a mean of 4.5, a standard
The Stewart Aviation Products Company uses a new production method to manufacture aircraft altimeters. A random sample of 81 altimeters resulted in errors with a standard deviation of s = 52.3 ft. At the 0.05 level of significance, test the claim that the new production line has errors with a
The incubation periods for different, common bird families of the type Hole Nesters have a standard deviation of 6.8 days. The incubation periods for a sample of five different, common bird families of the type Open Nesters have a standard deviation of 2.0. Use a 0.05 significance level to test the
With individual lines at its various windows, the Humber Valley Credit Union found that the standard deviation for normally distributed waiting times on Friday afternoons was 6.2 min. The credit union experimented with a single main waiting line and found that for a random sample of 25 customers,
Do men's heights vary more than women's? The nurse at a women's college has collected data from physical exams. The standard deviation of women's heights is found to be 2.5 in. The college has now become coed and the first 20 male students have heights with a standard deviation of 2.8 in. Use a
Xtron Electrics manufactures dental X-ray tubes. Health Canada has warned that they are not fulfilling regulations for Radiation Emitting Devices. For a sample of 20 X-ray tubes in operation, their mean peak-value voltage ( = 52 kV) is acceptable, but it is claimed that the standard deviation is
The St. Lawrence Investment Company finds that if the standard deviation for the weekly downtimes of their computer is 2 h or less, then the computer is predictable and planning is facilitated. Twelve weekly downtimes for the computer were randomly selected, and the sample standard deviation was
The Medassist Pharmaceutical Company uses a machine to pour cold medicine into bottles in such a way that the standard deviation of the weights is 0.15 oz. A new machine was tested on 71 bottles, and the standard deviation for this sample is 0.12 oz. The Dayton Machine Company, which manufactures
a. H1: µ < 27.3 n = 10 α = 0.05 b. H1: p ≠ 0.5 n = 150 α = 0.01 c. H1: σ ≠ 15 n = 20 α = 0.05 Find the appropriate critical values. In all cases, assume that the population standard deviation σ is unknown.
The Medassist Pharmaceutical Company makes a pill intended for children susceptible to seizures. The pill is supposed to contain 20.0 mg of Phenobarbital. A random sample of 20 pills yielded the amounts (in milligrams) listed here. Are these pills acceptable at the Î± = 0.01
Has the number of times the House sits in each session of federal Parliament grown more variable? The overall standard deviation of days the House sits per Parliament is 188.3. But in a sample of nine Parliaments since World War II, the standard deviation of days the House sits per Parliament is
a. H0: µ = 19.9 n = 40 α = 0.10 b. H0: σ ≤ 0.93 n = 10 α = 0.025 c. H0: p ≥ 0.25 n = 540 α = 0.01 Find the appropriate critical values. In all cases, assume that the population standard deviation σ is unknown.
The claim that statistics consultants have a mean income of $90,000 is to be tested at the 0.05 significance level. Respond to each of the following: a. Give the null hypothesis in symbolic form. b. Is this test left-tailed, right-tailed, or two-tailed? c. In simple terms devoid of symbolism and
The claim that lengths of CBC commercials have a standard deviation less than 15 s is to be tested at the 0.01 significance level. Respond to each of the following: a. Give the null hypothesis in symbolic form. b. Is this test left-tailed, right-tailed, or two-tailed? c. In simple terms devoid of
According to the National Population Health Survey for 1996-97, 28% of those with dental insurance did not have their teeth checked during the surveyTesting a Claim About a Mean, Proportion, Standard Deviation, or Variancewith dental insurance. Test the claim that more than one quarter (25%) of
A Telektronics dental X-ray machine bears a label stating that the machine gives radiation dosages with a mean of less than 5.00 mill roentgens (mR). Sample data consist of 36 randomly selected observations with a mean of 4.13 mR and a standard deviation of 1.91 mR. Using a 0.01 level of
Using the same sample data from Exercise 6, use a 0.01 significance level to test the claim that the radiation dosages have a standard deviation less than 2.50 mR. What is a practical consequence of a standard deviation that is too high in this case?
In the 1991 Census of Agriculture, 26.7% of all farms had gross farm receipts over $100,000. In a more recent sample of 75 farms, 23 had that level of gross income. Using the 0.01 level of significance, test the claim that the proportion of farms with gross farm receipts over $100,000 is greater
The Cape Breton Bottling Company distributes cola in cans labeled 355 mL. Measurement Canada randomly selected 24 cans, measured their contents, and obtained a sample mean of 348.69 mL and a sample standard deviation of 11.21 mL. Use a 0.01 significance level to test the claim that the company is
For healthy women aged 18-24, systolic blood pressure readings (in millimeters of mercury) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.a. If a healthy woman is randomly selected from the general population of all women aged 18-24, find the probability of getting
A medical researcher obtains the systolic blood pressure readings (in millimeters of mercury) in the accompanying list for women aged 18-24 who have a new strain of viral infection. (As in Exercise 1, healthy women in that age group have readings that are normally distributed with a mean of 114.8
A student majoring in psychology designs an experiment to test for extrasensory perception (ESP). In this experiment, a card is randomly selected from a shuffled deck, and the blindfolded subject must guess the suit (clubs, diamonds, hearts, spades) of the card selected. The experiment is repeated
An important requirement in Sections 7-4 and 7-6 is that the sample data must come from a population that is normally distributed. a. Refer to the body temperatures of females listed in Data Set 18 of Appendix B and construct a stem-and-leaf plot. b. Based on the result, does the distribution
In Exercises 1 and 2, assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µd = 0. Assuming α 0.05 level of significance, find (a) d, (b) sd, (c) the it test statistic, and (d) the critical values.
In May 1997, Calgary-based Bre-X Minerals collapsed when its gold assets were revealed to be dramatically less than had been claimed. Did this collapse affect the prices of other mining stocks?a. Using the price data below, construct a 98% confidence interval for the mean difference of their
Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in
If a t test were run on Excel at the 0.01 confidence level, using the data in Exercise 10, the following output would be produced.Could a person who ran this test validly reject a null hypothesis that there is no difference in means? Is this the same answer as is reached in Exercise 10(b)? If not,
Refer to Data Set 2 in Appendix B. Use the paired data consisting of the body temperatures of "initially standing" subjects in the standing posture (column STANDI) and after lying down (column SUPINE2). a. Construct a 95% confidence interval for the mean difference of the STANDI temperatures minus
A company offers a daily list of stock picks to paid subscribers. Its "Track Record for TSE" web page shows the prices of stocks it has recornmended (1) on the day the "buy" recommendation was made, and (2) on a subsequent day within the next week or two. The accompanying table is a sample from
Re-examine the data presented in Exercise 7. Is there any data value that may possibly be an outlier? How would the results be affected if that value were excluded from the analysis? In general, can an outlier have a dramatic effect on the hypothesis test and confidence interval?
Exercise 13 used temperatures given in degrees Celsius. Suppose we express all of the temperatures in their equivalent Fahrenheit value. Is the hypothesis test affected by such a change in units? Is the confidence interval affected by such a change in units? How?
The 95% confidence interval for a collection of paired sample data is 0.0 < μd < 1.2. Based on this confidence interval, the traditional method of hypothesis testing leads to the conclusion that the claim of μd > 0 is supported. What is the smallest possible value of the significance level of the
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Using the sample paired data in Exercise 1, construct a 95% confidence interval for the population mean of all differences x - y.
Using the sample paired data in Exercise 2, construct a 99% confidence interval for the population mean of all differences x - y.
Do strong El Nino phenomena change the weather as much as people claim?a. Using the data in the following table (aggregate temperature departures from spring norms in degrees Celsius), test the claim that the progression of a strong El Nino, from the spring of onset to the next spring, affects
Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings (in millimeters of mercury) were measured before and after the drug was taken, with the results given in the accompanying table.a. Use the sample data to
Does past growth in a company translate to continued growth in the future? In 1988, Profit magazine identified the 50 fastest-growing companies in Canada. In 1998, it revisited these companies. Of the companies for which relevant data were available, 10 have been randomly selected. Compare their
According to a report in The Globe and Mail, the Canadian oil and gas industry "ramped up" investment spending in the period from 2000 to 2001 ("Energy Sector Ramps Up Spending," The Globe and Mail, January 29, 2001, p. B14). The accompanying table shows the spending levels (in millions of dollars)

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