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

A study was conducted to examine differences in starting salaries for university graduates in Ontario and Quebec. Because starting salaries are in different ranges based on type of degree, the Ontario and Quebec results are paired with respect to degree earned in the adjacent table.a. At the 0.05
In Exercises 1, use a 0.05 significance level to test the claim that the two samples come from populations with the same mean. In each case, the two samples are independent and have been randomly selected.
A fish-processing company is concerned about the shelf life of its new cat food. A sample examined in Halifax, Nova Scotia (n = 35) had an acceptable mean shelf life of 13 months, with a standard deviation of 1.44 months. But a second sample, examined in Dartmouth, Nova Scotia (n - 40), had a mean
Data Set 9 in Appendix B contains measured levels of serum cotinine (in ng/mL) for two samples of nonsmokers: nonsmokers with no environmental tobacco smoke exposure at home or at work, and nonsmokers who are exposed to environmental tobacco smoke at home or at work. a. Testing at the 0.02 level of
Data Set 11 in Appendix B contains weights of 100 randomly selected M&cM plain candies. Those weights have a mean of 0.9147 g and a standard deviation of 0.0369 g. A previous edition of this book used a different sample of 100 M&M plain candies, with a mean and standard deviation of 0.9160 g and
Two samples are used to compare building permit values for larger communities versus smaller ones in the regional municipality of Durham, in Ontario. For both samples n is 38. Expressed in thousands of dollars, the mean value per building permit for the larger communities is 102.008, with a
As an aid to farmers, the Alberta government records freezing dates for over a hundred locations around the province. Based on average last-frost dates for spring, a researcher has proposed dividing the province into early last-frost locations and late last-frost locations. Refer to Data Set 17 of
Refer to the pulse rates in Data Set 8 from Appendix B. First identify and delete the two outliers that .are unrealistic pulse rates for living and reasonably healthy statistics students. a. Use a 0.05 level of significance and the traditional method of testing hypotheses to test the claim that
When testing for a difference between the means of a treatment group and a group given a placebo, the following Excel display is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (Variable 1) comes from a population with a mean
When testing for a difference between the means of a treatment group and a group given a placebo, the following Excel display is obtained. Using a 0.02 significance level, is there sufficient evidence to support the claim that the treatment group (Variable 1) comes from a population with a mean
Refer to Exercise 5. If the actual difference between the population means is 1.5, find Î², the probability of a type II error. (See Section 7-2.) Hint: In Step 1, replace x- by (x-1 - x-2),Replace Î¼x- by 0, and replace Ïƒ x- by
The examples in this section used the axial loads of a sample of cans 0.0109 in. thick and a second sample of cans 0.0111 in. thick. (The original data are listed in Data Set 15 of Appendix B.) We noted that the second sample includes an outlier of 504 lb. How are the box plots, the hypothesis
In Exercises 2, use a 0.05 significance level to test the claim that the two samples come from populations with the same mean. In each case, the two samples are independent and have been randomly selected.
The examples in this section used the axial loads of cans, where the loads were given in pounds. How are the box plots, hypothesis test, and confidence interval affected if the loads are all converted to kilograms?
a. Find the variance for this population of x scores: 5,10, 15. (See Section 2-5 for the variance σ2 of a population.) b. Find the variance for this population of y scores: 1, 2, 3. c. List the population of all possible differences x - y, and find the variance of this population. d. Use the
Using the sample data given in Exercise 1, construct a 95% confidence interval estimate of the difference between the two population means. Do the confidence interval limits contain 0? What do you conclude about the difference between the control group and experimental group?
Using the sample data given in Exercise 2, construct a 95% confidence interval estimate of the difference between the two population means. Do the confidence interval limits contain 0? What do you conclude about the difference between the math majors and the English majors?
For comparison purposes, mutual funds are often grouped into various categories. Do Canadian equity funds and Canadian balanced equity funds differ with respect to percentage of foreign holdings within the funds? a. Using the data shown, and a 0.01 level of significance, test the claim that there
Provincial governments across Canada have been re-examining their delivery of services, such as health care. A researcher compared the number of beds in long-term care centres in New Brunswick and in Nova Scotia. Her sample results are summarized in the margin, based on data in Guide to Canadian
The Medassist Pharmaceutical Company wants to test Dozenol, a new cold medicine intended for night use. Tests for such products often include a "treatment group" of people who use the drug and a "control group" of people who don't use the drug. Fifty people with colds are given Dozenol, and 100
A group of college students randomly selected 217 student cars and found that they had ages with a mean of 7.89 years and a standard deviation of 3.67 years. They also randomly selected 152 faculty cars and found that they had ages with a mean of 5.99 years and a standard deviation of 3.65
In April 1996, The Globe and Mail listed the salaries of the hundreds of University of Toronto staff who earn at least $100,000 annually. On studying this article, several disgruntled staff (whose last names begin with S, V, and Q) concluded that top staff whose names begin with S to Z earn less
In Exercises 1, test the given claim. Use a significance level of a = 0.05, and assume that all populations are normally distributed. Use the traditional method of testing hypotheses outlined, and draw the appropriate graphs. Claim: Populations A and B have different variances (a2 ^ o~2). Sample
Provincial governments across Canada have had to re-examine their delivery of services, such as health care, to avoid expensive duplication, and yet provide fair access to their citizens. The following table is based on one random sample of hospitals in New Brunswick and another in Nova Scotia, and
Sample data were collected to compare the ages of CEOs of top growth companies in western Canada and Quebec. Because of small sample sizes, techniques introduced later in this chapter would be needed to compare group means. One such method assumes equal variances for the two groups. At the 0.05
Refer to Data Set 11 in Appendix B and use a 0.10 level of significance to test the claim that red and yellow M&M plain candies have weights with different standard deviations. If you were responsible for controlling production so that red and yellow M&cMs have weights with the same amount of
A hypothesis test of the claim a\ = cr1 is being conducted with a 0.05 level of significance. What do you conclude in each of the following cases? a. Test statistic is F = 2.0933; n1 = 50; n2 = 35 b. Test statistic is F = 1.8025; n1 = 50; n2 = 35 c. Test statistic is F = 2.3935; n1 = 40; n2 = 20
To test a claim about two population variances by using the P-value approach, first find the F test statistic, then refer to Table A-5 to determine how it compares to the critical values listed for α = 0.01, = 0.025, and α = 0.05. For example, if the F test statistic (for a one-tailed test) is
For hypothesis tests in this section that were two-tailed, we found only the upper critical value. (Recall that for two-tailed tests, the significance level that you look up in the F distribution tables is in fact a/2.) Let's denote that value by FR, where the subscript suggests the critical value
In addition to testing claims involving Ïƒ12 and Ïƒ22, we can also construct interval estimates of the ratio Ïƒ12/Ïƒ22 using the following expression:Here FL and FR are as described in Exercise 15. Construct the 95% confidence interval estimates for the
Sample data consist of temperatures recorded for two different groups of items that were produced by two different production techniques. A quality control specialist plans to analyze the results. She begins by testing for equality of the two population standard deviations.a. If she adds the same
In Exercises 2, test the given claim. Use a significance level of a = 0.05, and assume that all populations are normally distributed. Use the traditional method of testing hypotheses outlined, and draw the appropriate graphs. Claim: Population A has a larger variance than population B. Sample A: n
An experiment was conducted to investigate the effect of stress on the recall ability of police eyewitnesses. The experiment involved a non stressful interrogation cooperative suspect and a stressful interrogation of an uncooperative and belligerent suspect. The numbers of details recalled a week
Customer waiting times are studied at the Humber Valley Credit Union. When 25 randomly selected customers enter any one of several waiting lines, their times have a mean of 6.896 min and a standard deviation of 3.619 min. When 20 randomly selected customers enter a single main waiting line that
A study was done of 137 young adult males who had been treated for substance abuse. The study compared their yearly rates of traffic accidents before treatment and after treatment. For the pre-treatment group, the mean accident rate was 0.123, with a standard deviation of 0.167. For the
Canadian equity funds and Canadian balanced equity funds can be compared for their percentages of foreign holdings. At the 0.05 significance level, test the claim that both types of funds have the same variance.Based on data from mutual funds>Mutual Funds Update, published by the Bank of Montreal,
A fish-processing company is concerned about the shelf life of its new cat food. A sample examined in Halifax (n = 35) had an acceptable mean shelf life of 13 months, with a standard deviation of 1.44 months. But a second sample, examined in Dartmouth (n - 40), had a mean shelf life of only 11
An investor is comparing the variability of estimates by stock analysts, when they analyze the earnings potentials of U.S. and Canadian firms. For a sample of estimates (by different analysts) of the earning potentials of Canadian firms, the standard deviation is 0.0204, whereas the standard
Because of wind patterns, Air Canada flights between Vancouver and San Francisco can take different times in each direction. Sample times for flights between these cities, from March 8 to March 18, 1997, are shown. Test the claim that both sets of times come from populations with the same variance.
In Exercises 1, test the given claim. Use a significance level of Î± = 0.05, and assume that all populations are normally distributed. Use the traditional method of testing hypotheses outlined in Figure 7-4.Claim: Populations A and B have the same mean (/A, = /n,). Sample A: «, =
A simple random sample of 21 peanut M&M candies is selected, and each candy is weighed. The mean is 2.4658 g and the standard deviation is 0.3127 g. The 100 g MScM plain candies listed in Data Set 11 in Appendix B have a mean of 0.9147 g and a standard deviation of 0.0369 g. Is there sufficient
Data Set 11 in Appendix B includes a sample of 21 red M&Ms with weights having a mean of 0.9097 g and a standard deviation of 0.0275 g. The data set also includes a sample of 8 orange M&Ms with weights having a mean of 0.9251 g and a standard deviation of 0.0472 g. Use a 0.05 level of significance
Refer to Data Set 11 in Appendix B and test the claim that yellow M&Ms and green M&Ms have the same mean weight. If you were part of a quality control team with responsibility for ensuring that yellow M&Ms and green M&Ms have the same mean weight, would you take corrective action?
Refer to Data Set 4 in Appendix B. If the Ontario-Manitoba border is taken as the boundary between East and West, test the claim that in comparing provincial averages, there is no difference in mean annual precipitation between western and eastern provinces. Use the 0.05 level of significance.
Provincial governments have been re-examining their delivery of services, such as health care. The accompanying table is based on one random sample of hospitals in New Brunswick and another in Nova Scotia, and shows the total number of beds in each hospital (Guide to Canadian Healthcare Facilities,
Sample data were collected to compare the ages of CEOs of top growth companies in western Canada and Quebec, shown in the table below. Exercise 11 in Section 8 - 4 looked at the variances for these two groups. Assuming the populations have equal variances, test at the 0.05 significance level the
An experiment was conducted to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of people who drank ethanol and another group given a placebo. The results are shown in the accompanying table. Use a 0.05 significance level to test the
An experiment was conducted to test the effects of alcohol. The breath alcohol levels were measured for a treatment group of people who drank ethanol and another group given a placebo. The results are given in the accompanying table. Use a 0.05 significance level to test the claim that the two
Assume that two samples have the same standard deviation and that both are independent, small, and randomly selected from normally distributed populations. Also assume that we want to test the claim that the samples come from populations with the same mean. a. Is it necessary to conduct a
Refer to the two examples of this section that used the number of employees in key industry groups. How are the hypothesis test and confidence interval affected if the number of degrees of freedom is calculated with Formula 8-1, instead of using the smaller of n1 - 1 and n2 -1?
In Exercises 2, test the given claim. Use a significance level of a = 0.05, and assume that all populations are normally distributed. Use the traditional method of testing hypotheses outlined in Figure 7-4.
Suppose that the sample data for the ages of CEOs displayed for Exercise 15 had omitted one data point because it was viewed as an outlier. This extra data value was an 11th CEO from Quebec, who is 80. How are the hypothesis test and confidence interval affected if this apparently extreme value is
Using the sample data in Exercise 1, construct a 95% confidence interval estimate of the difference between the means of the two populations.
Using the sample data in Exercise 2, construct a 95% confidence interval estimate of the difference between the means of the two populations.
The equality of Air Canada flight times (in hours) between Vancouver and San Francisco is tested using Excel. A preliminary F test shows that there is no significant difference between the two sample variances, so, as shown in the accompanying figure (a = 0.05), the t test assuming equal variances
Employees who work with electronic components at Canadian Automated Electronics are required to undergo special training. Training includes completing tasks under simulated conditions and recording completion times. A supervisor claims he has found some star performers among a new group of
In a sample of the driving records of 137 young adult males who underwent treatment for substance abuse in a Toronto clinic, the mean accident rate after treatment was 0.068, with a standard deviation of 0.223 (based on data from "Does Treatment of Substance Abuse Improve Driving Safety? A
Assume that Data Set 21 in Appendix B represents sample prices and characteristics of high-quality diamonds sold at auction. A vendor claims that near - colorless diamonds sell at a higher price than yellower ones. Based on the data summarized in the margin (from Data Set 21, with colours 5-9
Assume that Data Set 21 in Appendix B represents sample prices and characteristics of high quality diamonds sold at auction. A vendor claims that nearly flawless diamonds sell at a higher price than noticeably flawed ones. Based on the data summarized in the margin (from Data Set 21, with clarity
In Exercises 1, assume that you plan to use a significance level of a - 0.05 to test the claim that p1.= p2. Use the given sample sizes and numbers of successes to find(a) The pooled estimate p-,(b) The z test statistic,(c) The critical z values, and(d) The P-value.
During the campaign for the June 1997 federal election, many opinion polls were conducted. Early in the campaign, a poll found that 47.6% of voters supported the Liberals. Then in May 1997 an Angus Reid poll found that of 3208 voters surveyed, 42% supported the Liberals (based on a report conducted
Karl Pearson, who developed many important concepts in statistics, collected crime data in 1909. Of those convicted of arson, 50 were drinkers and 43 abstained. Of those convicted of fraud, 63 were drinkers and 144 abstained. Use a 0.01 significance level to test the claim that the proportion of
An initial public offering (IPO) of a company's stock is considered "under-priced" if there is a large percentage difference between its issuing price and its closing price after one day of trading. A Canadian study based on a sample of 399 IPOs, over 25 years, showed that approximately 8% of those
Professional pollsters are becoming concerned about the growing rate of refusals among potential survey subjects. In analyzing the problem, there is a need to know if the refusal rate is universal or if there is a difference between the rates for central-city residents and those not living in
A mining company conducted a safety analysis for workers at a Saskatchewan site. Of 450 sample records in January, 16 revealed undesirable safety conditions. Of 660 sample records in February/March, 10 showed undesirable conditions. Is there sufficient sample evidence to support the site manager's
When games were sampled from throughout a season, it was found that the home team won 127 of 198 professional basketball games, and the home team won 57 of 99 professional football games (based on data from "Predicting Professional Sports Game Outcomes from Intermediate Game Scores," by Cooper et
Ziac is a Lederle Laboratories drug developed to treat hypertension. Lederle Laboratories reported that when 221 people were treated with Ziac, 3.2% of them experienced dizziness. It was also reported that among the 144 people in the placebo group, 1.8% experienced dizziness.a. Can you use the
To test the null hypothesis that the difference between two population proportions is equal to a nonzero constant c, use the test statisticAs long as n1, and n2 are both large, the sampling distribution of the test statistic z will be approximately the standard normal distribution. Refer to the
Sample data are randomly drawn from three independent populations, each of size 100. The sample proportions are p^1 = 40/100, p^2 = 30/100, and p3 = 20/100.a. At the 0.05 significance level, test H0: p1 = p2.b. At the 0.05 significance level, test H0: p2 = p3.c. At the 0.05 significance level, test
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - a can be found as follows. In the expressionReplace n1 and n2 by n (assuming that both samples have the same size) and replace each of a p1 , q2, p2 and
In Exercises 2, assume that you plan to use a significance level of a - 0.05 to test the claim that p1. = p2. Use the given sample sizes and numbers of successes to find(a) The pooled estimate p-,(b) The z test statistic,(c) The critical z values, and(d) The P-value.
The Composting Council of Canada requires that type AA compost must comprise less than 1% foreign matter. A ministry inspector uses random sampling to test two commercial composting facilities against the standards. Of 50 samples collected at Facility A, 15 had less than half of the allowable level
According to the Annual Report of the Correctional Investigator (1995-1996), this agency was able to resolve or provide assistance for 88 of the 280 complaints received about the prison grievance procedure. On the other hand, they were able to resolve or provide assistance for 55 of 232 complaints
Based on a random survey of 1000 adult Canadians conducted in January 2001, a headline in The Globe and Mail (February 5, 2001) concluded that "fewer Canadians support free trade." In the survey, 64% of the respondents supported the North American free trade agreement, but in a 1999 survey 70%
In initial tests of the Salk vaccine, 33 of 200,000 vaccinated children later developed polio. Of 200,000 children vaccinated with a placebo, 115 later developed polio. At the 0.01 level of significance, test the claim that the Salk vaccine is effective in lowering the polio rate. Does it appear
A random sample was taken from the Financial Post list of top 500 companies for 1998. Of 26 food- and beverage-related industries in the sample, 12 had at least 10% foreign ownership. Of 29 wholesale distribution firms in the sample, 15 had at least 10% foreign ownership. a. Use a 0.01 significance
In a study of people who stop to help drivers with disabled cars, researchers hypothesized that more people would stop to help someone if they first saw another driver with a disabled car getting help. In one experiment, 2000 drivers first saw a woman being helped with a flat tire and then saw a
Data Set 18 in Appendix B shows body temperatures (in degrees Celsius) of adults accepted for voluntary surgical procedures in an urban hospital. Sample data for men are summarized by these statistics: n = 12, x- = 36.275, s = 0.561. Sample data for women are summarized by these statistics: n = 12,
Twelve Dozenol tablets are tested for solubility before and after being stored for one year. The indexes of solubility are given in the table below.a. At the 0.05 significance level, test the claim that the Dozenol tablets are more soluble after the storage period. b. Construct a 95% confidence
In clinical tests of adverse reactions to the drug Viagra, 7% of the 734 subjects in the treatment group experienced dyspepsia (indigestion), but 2% of the 725 subjects in the placebo group experienced dyspepsia (based on data from Pfizer Pharmaceuticals). a. Is there sufficient evidence to support
Having just been charged more to fly from Toronto to Saint John than from Toronto to Britain, an annoyed passenger claims there is no difference in price between domestic and international flights. Using ads in the Toronto Star, his travelling companion compiles a random sample of prices for
To conduct the means test in Exercise 4, it was assumed that the two samples had unequal variances. Test whether the evidence supports that assumption, at the 0.02 level of significance.
A test question is considered good if it discriminates between prepared and unprepared students. The first question on a test was answered correctly by 62 of 80 prepared students and by 23 of 50 unprepared students. At the 0.05 level of significance, test the claim that this question was answered
In a study of techniques used to measure lung volumes, physiological data were collected for 10 subjects. The values given in the accompanying table are in liters, representing the measured forced vital capacities of the 10 subjects in a sitting position and in a supine (lying) position. At the
A major airline is experimenting with its training program for flight attendants. With the traditional six-week program, a random sample of 60 flight attendants achieves competency test scores with a mean of 83.5 and a standard deviation of 16.3. With a new ten-day program, a random sample of 35
Researchers are testing commercial air-filtering systems made by the Winston Industrial Supply Company and the Barrington Filter Company. Random samples are tested for each company, and the filtering efficiency is scored on Winston Barrington a standard scale, with the results shown in the margin.
The data in the table to the right were obtained through a survey of randomly selected subjects. a. If one of the survey subjects is randomly selected, find the probability of getting someone ticketed for speeding. b. If one of the survey subjects is randomly selected, find the probability of
The Newton Scientific Instrument Company manufactures scales with its day shift and night shift. Random samples are routinely tested with errors recorded as positive amounts for readings that are too high or negative for readings that are too low. a. A random sample of 40 scales made by the day
Analysis of variance results generated by Excel are given on the next page. The sample results are measured consumer reactions to television commercials for different products. Assume that we want to use a 0.05 significance level in testing the null hypothesis that the different products have
The values in the list below are measured maximum breadths of male Egyptian skulls from different epochs (in mm, based on data from Ancient Races of the Thebaid, by Thomson and Randall-Maciver). Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a
A political scientist claims that since Confederation, the number of times the House of Commons sits in each session of Parliament has been increasing. The table shows, in three samples grouped by Parliament number, how many times the House of Commons has sat in each Parliament. Parliaments lasting
The political scientist from Exercise 11 also claims that for Parliaments of 4, 4.5, and 5 years in length, the mean number of times the Senate has sat during a session is equal. The table shows, in three samples grouped by length in years, the number of times that the Senate has sat in each
Refer to Data Set 21 in Appendix B. At the 0.05 significance level, test the claim that the mean weight (in carats) of diamonds is the same for each of the four clarity levels (2, 3, 4, or 5) shown. If you need to save money by compromising on clarity, does this necessarily limit the carat of the
Refer to Data Set 9 in Appendix B. Use a 0.01 significance level to test the claim that the mean cotinine level is different for these three groups: non-smokers not exposed to environmental tobacco smoke, nonsmokers who are exposed to tobacco smoke, and people who smoke. What do the results suggest
Repeat Exercise 3 after adding 1°C to each temperature listed in the "Awaiting Surgery" group. Compare these results to those found in Exercise 3.
If Exercise 3 is repeated after changing the temperature readings from the Celsius scale to the Fahrenheit scale, are the results affected? In general, how is the analysis of variance F test statistic affected by the scale used?
How are analysis of variance results affected in each of the following cases?a. The same constant is added to every sample score.b. Every sample score is multiplied by the same constant.c. The order of the samples is changed.
Five independent samples of 50 scores each are randomly drawn from popu¬lations that are normally distributed with equal variances. We wish to test the claim that μ1 = μ2 = μ3 = μ4 = μ5 a. If we used only the methods given in Chapter 8, we would test the individual claims μ1 = μ2 =
In this exercise you will verify that when you have two sets of sample data, the t test for independent samples (assuming equal variances) and the ANOVA method of this section are equivalent. Refer to the data used in Exercises 5-7, but exclude the data on conglomerates. a. Use a 0.05 level and the
Analysis of variance results generated by Excel are given on the next page. The sample results are measured consumer reactions to television commercials for different products. Assume that we want to use a 0.05 significance level in testing the null hypothesis that the different products have

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