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mathematics
statistics

Questions and Answers of Statistics

Refer to Data Set 20 in Appendix B. If annual person-days lost due to work stoppages from 1976 to 1999 are analyzed, for six groups of transportation industries, the median annual number of
Exercise 1; α = 0.05Refer to the sample data for the given exercises in Section 12-2. Instead of the sign test, use the Wilcoxon signed-ranks test to test the claim that both samples come from
Assume that the Wilcoxon signed-ranks test is being used for a two-tailed hypothesis test with a significance level of 0.05. a. With n = 10 pairs of data, find the lowest and highest possible values
Exercise 2; α = 0.05 Refer to the sample data for the given exercises in Section 12-2. Instead of the sign test, use the Wilcoxon signed-ranks test to test the claim that both samples come from
Exercise 8; α = 0.01 Refer to the sample data for the given exercises in Section 12-2. Instead of the sign test, use the Wilcoxon signed-ranks test to test the claim that both samples come from
Exercise 11; α = 0.01Refer to the sample data for the given exercises in Section 12-2. Instead of the sign test, use the Wilcoxon signed-ranks test to test the claim that both samples come from
A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given below. The measurements are in centimetres on a pain scale. At
In a study of the effect of posture on body temperature, data were collected for 11 subjects. The values given in the table are in degrees Celsius and represent the measured body temperatures of the
According to a paid promotional article in The Globe and Mail, installation of an automotive accessory called the Platinum Vapour Injector (P.V.I.) can significantly increase a vehicle's gas mileage.
A company offers a daily list of stock picks to paid subscribers. Its website, called Track Record for TSE, shows the prices of stocks. it has recommended (1) on the day the "buy" recommendation was
In an exercise in Chapter 7, the claim that chickens fed with enriched feed attain a mean weight greater than 1.77 kg was tested. In an experiment with an enriched feed mixture, nine chickens are
The example in this section tested the null hypothesis that red and yellow M&M plain candies have weights with identical populations. Refer to Data Set 11 in Appendix B and test the claim that red
The Mann-Whitney L7 test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that it applies to the same situations and always leads to the same conclusions. In the
Assume that we have two treatments (A and B) that produce measurable results, and we have only two observations for Treatment A and two observations for Treatment B. We cannot use the test statistic
When using the Wilcoxon rank-sum test, is the effect of an outlier large or small? Explain.
Listed below are time intervals (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park. Using a 0.05 significance level, test the claim that the times are the same for
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
An umbrella maker is deciding whether to concentrate on eastern or western Canada. To help decide, she randomly selects cities from both parts of the country, and obtains the corresponding annual
The "bootstrap" (simulated) samples below are based on summary data for building statistics, in The Durham Business News, June 1998. They show the values of building permits, in thousands of dollars,
Sample data were collected in a study of calcium supplements and their effects on blood pressure. A placebo group and a calcium group began the study with measures of blood pressures. At the 0.05
The arrangement of test items was studied for its effect on anxiety. Sample results are as follows:At the 0.05 level of significance, test the claim that the two samples come from populations with
Refer to Data Set 9 in Appendix B. Use a 0.01 significance level to test the claim that the population of cotinine levels is the same for these two groups: Nonsmokers who are not exposed to
Two separate classes of 6 and 8 were taught the same subject using different pedagogies. The final marks of the students were as follows:No assumptions about the normality of the data were made. Is
The accompanying table lists the numbers of House sittings in each of 18 Parliaments, randomly selected from three different time periods. Parliaments lasting less than a year were not sampled. Using
a. In general, how is the value of the test statistic H affected if a constant is added to (or subtracted from) each score? b. In general, how is the value of the test statistic H affected if each
For three samples, each of size 5, what are the largest and smallest possible values of H?
In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H byHere T = t3 - t, where t is the number of observations that are tied for
Show that for the case of two samples, the Kruskal-Wallis test is equivalent to the Wilcoxon rank-sum test. This can be done by showing that for the case of two samples, the test statistic H equals
Has usage of the Internet increased? Very likely, more people are using the Internet than in the past, especially from home. But if a person has been using the Internet all along, are they are now
Refer to Data Set 21 in Appendix B. A desirable trait for a top-rate diamond is to be flawless. Clarity is a measure of this characteristic-with 1 being the best. At the 0.05 level, test the claim
Flammability tests were conducted on children's sleepwear. The Vertical Semi restrained Test was used, in which pieces of fabric were burned under controlled conditions. After the burning stopped,
Refer to Data Set 11 in Appendix B. At the 0.05 significance level, test the claim that the weights of M&Ms are the same for each of the six different colour populations. If it is the intent of Mars,
Refer to Data Set 9 in Appendix B. Use a 0.01 significance level to test the claim that the populations of cotinine levels are identical for these three groups: nonsmokers who are not exposed to
The accompanying table lists the lengths, in minutes, and star ratings of televised movies rated 18 +. Use a 0.05 significance level to test whether there is any difference in movie length based on
The City Resource Recovery Company (CRRC) collects the waste discarded by households in a region. Discarded waste must be separated into categories of metal, paper, plastic, and glass. In planning
For a store with 3 locations, daily sales (in thousands) were taken from each location for a series of dates:Is there any significant difference in median daily sales between the 3 locations? Test at
For each of the following samples of paired ranks, sketch a scatter diagram, find the value of rs, and state whether there appears to be a correlation between x and y.a.b.c.
An amateur biologist has read that the lifespans of mammals are related to their metabolic rates. The relation, if any, is not linear, so she will test the claim based on the rank correlation
The accompanying table lists educational requirements (in years) and typical salary (in thousands of dollars) for a sample of professions. Based on the result, can you expect to earn more if you
Refer to Data Set 21 in Appendix B and use the paired data for the price and weight (carats) of diamonds. Is there a correlation, suggesting that heavier diamonds are generally of greater value? Use
Refer to Data Set 16 in Appendix B and use the paired data for durations and intervals after eruptions of the Old Faithful geyser. Is there a correlation, suggesting that the interval after an
Refer to Data Set 16 in Appendix B and use the paired data for intervals after eruptions and heights of eruptions of the Old Faithful geyser. Is there a correlation, suggesting that the interval
Refer to Data Set 2 in Appendix B and use the paired data consisting of the first and second columns of body temperatures for subjects who are initially sitting. Based on the result, does there
Refer to Data Set 2 in Appendix B and use the paired data consisting of the first and second columns of body temperatures for subjects who are initially standing. Based on the result, does there
Refer to Data Set 7 in Appendix B, which looks at temperature and precipitation departures from seasonal norms. Pick out the data pairs corresponding to years of strong El Ninos. Compare (a) the
Refer to Data Set 7 in Appendix B, which looks at temperature and precipitation departures from seasonal norms. Pick out the data pairs corresponding to years of strong El Ninos. Compare (a) the
One alternative to using Table A-9 involves an approximation of critical values for rs given asHere t is the t score from Table A-3 corresponding to the significance level and n - 2 degrees of
Find the critical value(s) for rs by using either Table A-9 or Formula 12-1, as appropriate. Assume two-tailed cases, where a represents the level of significance and n represents the number of pairs
a. How is rs affected if the scale for one of the variables is changed from feet to inches?b. How is rs affected if one variable is ranked from low to high while the other variable is ranked from
The accompanying table lists salary rankings and stress rankings for randomly selected jobs. Does it appear that salary increases as stress increases?Use the rank correlation coefficient to test the
Exercise 3 includes paired salary and stress level ranks for 10 randomly selected jobs. The physical demands of the jobs were also ranked; the salary and physical demand ranks are given below. Does
Ten jobs were randomly selected and ranked according to stress level and physical demand, with the results given below. Does there appear to be a relationship between the stress levels of jobs and
Most truck industry carriers operate within a single province or region. About 1% operates across multiple jurisdictions, including nationally. Comparing years ranked by total carrier activity (from
In studying the effects of heredity and environment on intelligence, scientists have learned much by analyzing the IQ scores of identical twins who were separated soon after birth. Identical twins
It's a baseball cliche that "pitching wins games." Test that claim based on the accompanying data. For eight randomly selected American League teams for the 2000 season, the following data compares
Researchers have studied bears by anesthetizing them in order to obtain vital measurements. The data in the table represent the first eight male bears in Data Set 3 from Appendix B.Use the rank
A A A B B B B B A A A A A A A Use the given sequence to determine the values of n1 n2, the number of runs G, and the 5% cutoff values from Table A-10.
As an aid to its farming industries, Alberta tracks the dates of last frost across the province. At some sites, the last frost occurs in mid-May, while others reach this event a month or more later.
Business trends and economics applications are often analyzed with the runs test. The accompanying list shows, in order by row, the net gain or loss in the S&P/TSX Composite Index (formerly the TSE
Listed below are the bonus numbers selected in consecutive Lotto 6/49 drawings. Test for randomness of odd (O) and even (E) numbers. What would lack of randomness mean for those who play the
The Restaurant Market Research Company hires Diana Kriplani to survey adults about their dining habits. A check of her first 40 results shows that their genders are represented in the following
Many mathematicians agree that the decimal digits of TT cannot be distinguished from any random sequence. Given below are the first 100 decimal places of TT. Test for randomness of odd (O) and even
Use the 100 decimal digits for TT given in Exercise 14. Test for randomness above (A) and below (B) the value of 4.5.
Test the claim that the sequence of World Series wins by American League and National League teams is random. Given below are recent results, with American and National League teams represented by A
Using the elements A, A, B, B, what is the minimum number of possible runs that can be arranged? What is the maximum number of runs? Now refer to Table A-10 to find the 5% cutoff G values for n1 = n2
a. Using all of the elements A, A, A, B, B, B, B, B, B, list the 84 different possible sequences. b. Find the number of runs for each of the 84 sequences. c. Use the results from parts (a) and (b) to
T F T F T F T F T F T T T T T T T T T T Use the given sequence to determine the values of n1 n2, the number of runs G, and the 5% cutoff values from Table A-10.
O O O O O O O O O O E E O O E E Use the given sequence to determine the values of n1 n2, the number of runs G, and the 5% cutoff values from Table A-10.
M F F F F M F F M M M F F F F F Use the given sequence to determine the values of n1 n2, the number of runs G, and the 5% cutoff values from Table A-10.
In conducting research for this book, one of the authors recorded the outcomes of a roulette wheel in the Stardust Casino. (Yes, it was hard work, but somebody had to do it.) Test for randomness of
The Niko Music Company uses a machine to produce compact discs that must meet certain specifications. When a sample of discs is selected in sequence from the assembly line, they are examined and
Natural Resources Canada reports regularly on seismic events (earthquakes) in Canada. In just the three days-January 15 to 17, 2001-there were 24 such events. Earthquake magnitudes are recorded in a
Test the claim that the sequence of World Series wins by American League and National League teams is random. Given below are recent results with American and National league teams represented by A
Since 1935, there have been 11 changes of prime minister in Canada, including Pierre Trudeau's re-election in 1980 after a period in Opposition. The political party of each new prime minister is
The accompanying table shows samples of data about Canadian prime ministers, popes, and British monarchs. The values are the numbers of years the subjects lived after they were first elected or were
A study was conducted to investigate some effects of physical training. Sample data (weights in kilograms) are listed in the margin. Use the sign test to test the claim that the training has no
Do Exercise 10 using the Wilcoxon signed-ranks test.Use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.
Two measures of health care are the mean number of people per physician, and the percentage of the population who reside fewer than 5 km from a physician. In the table below, the 10 provinces are
A focus group of people aged 18-24 were asked to rate 4 new video games on a scale from 1 to 10, 10 being best. These were the results:Is there any significant difference in the median ratings of the
A manufacturing firm wanted to determine if the median amount of waste per unit produced by a new type of lathe was significantly less than that of its current lathe. Samples from each lathe produced
A number of companies sell both cars and trucks in Canada. Do a company's car sales go up (or down) in tandem with its truck sales? The accompanying table shows the annual percent changes in car and
A Regina manufacturing company uses a machine to produce surgical knives that must meet certain specifications. A sample of knives is randomly selected and each knife is judged to be defective (D) or
The accompanying table shows a sample from poll results by The Globe and Mail Report on Business and Angus Reid, which compare CEO evaluations of the 25 top-performing firms over two years. For the
Internet search engines often return large lists of results for the search lists that are entered. Some guides suggest refining the search by adding more words to the search list. To test whether
The Medassist Pharmaceutical Company conducted a study to determine whether a drug affects eye movements. A standardized scale was developed, and the drug was administered to one group, while a
To test the effectiveness of the use of technology in a statistics course, four different sections were taught with different combinations of calculators and computer software, with final course
A statistics quiz consists of true-false questions with the answers listed as shown.a. Examine the sequence and try to identify a pattern showing that the answers are not random.b. What do you
A consumer investigator obtained prices from mail-order companies and computer stores. The accompanying lists show the prices (in dollars) quoted for cartons of floppy disks from various
The Broadbent Opinion Research Organization assigned a pollster to collect data from 30 randomly selected adults. As the data were submitted to the company, the genders of the interviewed subjects
The Kamloops Weight Clinic claims that everyone can lose weight after two weeks in its program. The following table lists the weights, in kilograms, of randomly selected clients before and after the
Refer to the annual numbers of person-days lost in the water-based transportation industry due to work stoppages in Data Set 20 in Appendix B. Find the following: a. Mean b. Median c. Mode d.
What is statistics?
Why would a statistician consider an inference incomplete without an accompanying measure of its reliability?
Explain the difference between a population and a process.
Define statistical thinking.
Suppose you're given a data set that classifies each sample unit into one of four categories: A, B, C, or D. You plan to create a computer database consisting of these data, and you decide to code
Suppose that a population contains 200,000 experimental units. Use a random number generator to select a simple random sample of n = 10 units from the population.
Zillow.com is a IH real estate Web site that provides free estimates of the market value of homes. A trio of University of Texas at San Antonio professors compared Zillow estimates to actual sale
The National Football League (NFL) is a lucrative business, generating an annual revenue of about $8 million. One key to becoming a financially successful NFL team is drafting a good quarterback (QB)
Pollsters regularly conduct opinion polls to determine the popularity rating of the current president. Suppose a poll is to be conducted tomorrow in which 2,000 individuals will be asked whether the

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