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mathematics
statistics

Questions and Answers of Statistics

Complete the following ANOVA table if it is known that there are three samples with sizes of 5, 7, and 7, respectively. Source of Sum of Squares Degrees of Mean
The following table is based on data in Data Sets 2 and 18 in Appendix B. Samples of human body temperatures in three contexts are compared. (Assume for this exercise that all three samples are
A large company is deciding between transportation methods for shipping its finished goods. Since the possibility of labour stoppages is a concern, a manager studied Data Set 20 in Appendix B for
At the 0.05 significance level, test the claim that the means of the revenues are the same in all three industry groups. Does any industry group seem to have higher revenues? If so, is this apparent
At the 0.05 significance level, test the claim that the means of the assets are the same in all three industry groups. Does any industry group seem to have greater assets?
At the 0.05 significance level, test the claim that the means of the numbers of employees are the same in all three industry groups. Does any industry group seem to have greater numbers of employees?
A disgruntled University of Toronto employee reads the list (published in The Globe and Mail) of U of T staff who earn over $100,000 annually. The employee claims that for staff in this category,
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,
Identify the indicated values.a. MS(interaction)b. MS(error)c. MS(Stars)d. MS(CTR)
Use the same data collected for Exercise 9, assume that pulse rates are not affected by an interaction between gender and smoking, and test the null hypothesis that gender has no effect on pulse
Use the same data collected for Exercise 9, assume that pulse rates are not affected by an interaction between gender and smoking, and test the null hypothesis that smoking has no effect on pulse
Use a statistics software package, such as Excel or SPSS/PC, that can produce results for two-way analysis of variance. First enter the data in the table used for Exercises 1-4 and verify that the
Refer to the data in the table used for Exercises 1-4 and subtract 10 from each table entry. Using a statistics software package with a two-way analysis of variance capability, determine the effects
Refer to the data in the table used for Exercises 1-4 and multiply each table-entry by 10. Using a statistics software package with a two-way analysis of variance capability, determine the effects of
In analyzing Table 9-3, we concluded that movie length is not affected by an interaction between star rating and CTR rating; it is not affected by star rating; and it is not affected by CTR
Find the test statistic and critical value for the null hypothesis of no interaction between star rating and CTR rating. What do you conclude?
Assume that the length of a movie is not affected by an interaction between its star rating and CTR rating. Find the test statistic and critical value for the null hypothesis that star rating has no
Assume that the length of a movie is not affected by an interaction between its star rating and CTR rating. Find the test statistic and critical value for the null hypothesis that CTR rating has no
Assuming that there is no effect on movie length from the interaction between star rating and CTR rating, test the null hypothesis that CTR rating has no effect on movie length. Identify the test
Assuming that there is no effect on movie length from the interaction between star rating and CTR rating, test the null hypothesis that star rating has no effect on movie length. Identify the test
Using a 0.05 significance level, test the claim of the hypothesis that the four operators have the same mean production output. Identify the test statistic and critical value, and state the
Using a 0.05 significance level, test the claim that the choice of machine has no effect on the production output. Identify the test statistic and critical value, and state the conclusion.
Refer to Data Set 8 in Appendix B and construct a table with pulse rates categorized according to the two factors of gender and whether the individual smokes. Select 9 scores for each cell and test
In a study of the effects of drinking and driving, 3 groups of adult men were randomly selected for an experiment designed to measure their blood alcohol levels after consuming 5 drinks. Members of
Is the mean cost of food items in a "typical" basket of products the same across Canada? The accompanying list shows the costs of the same items when purchased in four different cities. Do these
Twelve different 4-cylinder cars were tested for fuel consumption (in liters per 100 km) after being driven under identical highway conditions; the results are listed in the table and accompanying
Refer to the same data used in Exercise 3 and assume that fuel consumption is not affected by an interaction between engine size and type of transmission. Use a 0.05 level of significance to test the
Refer to the same data used in Exercise 3 and assume that fuel consumption is not affected by an interaction between engine size and type of transmission. Use a 0.05 level of significance to test the
Transport Canada is concerned about the braking performance of snowmobiles. The following table shows the distances in meters that snowmobiles took to stop when the brakes were applied. The results
The North of Superior Brewing Company plans to launch a major media campaign. Three advertising companies prepared trial commercials in an attempt to win a $2 million contract. The commercials were
The tread life in kilometers of a certain model of radial tire is normally distributed, with a mean of 60,000 km and a standard deviation of 5000 km (based on data from Goodyear).a. If one radial
Refer to the numbers of Newfoundland males in the labour force, in different SOC job categories, as listed in Data Set 14 in Appendix B.a. Find the mean.b. Find the standard deviation.c. Construct a
One common way to test for authenticity of data is to analyze the frequencies of digits. When people are weighed and their weights are rounded to the nearest pound, we expect the last digits 0, 1, 2,
The number 22/7 is similar to TT in the sense that they both require an infinite number of decimal places. However, 22/7 is a rational number because it can be expressed as the ratio of two integers,
In a "Scratch & Save" promotion, Zellers promised all customers a discount ranging from 5% to 50%, depending on the value that appeared on their "Scratch &c Save" card. In the accompanying table, the
In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Use the values listed here to test the claim that the actual frequencies
Refer to the Old Faithful geyser data in Data Set 16 of Appendix B. Test the claim that the time intervals are uniformly distributed among the five categories of 55-64, 65-74, 75-84, 85-94, 95-104.
Refer to Data Set 8 in Appendix B and record only the last digits of the pulse counts. Test for authenticity of the pulse counts by testing the claim that the last digits occur with equal frequency.
Refer to Data Set 10 in Appendix B and categorize the listed one-year returns for mutual funds as poor (up to 24%), fair (above 24% to 36%), good (above 36% to 48%), or excellent (above 48%). Test
Many lottery enthusiasts search for patterns that they hope will indicate winning combinations. Yuri thinks that sums of numbers in Lotto 6/49 draws are not evenly distributed. Refer to Data Set 12
In doing a test for the goodness-of-fit as described in this section, does an outlier have much of an effect on the value of the x1 test statistic? Test for the effect of an outlier by repeating
In doing a test for goodness-of-fit as described in this section, suppose that we multiply each observed frequency by the same positive integer greater than 1. How is the critical value affected? How
In this exercise we will show that a hypothesis test involving a binomial experiment is equivalent to a hypothesis test for a proportion (Section 7-5). Assume that a particular experiment has only
Excel can be used to generate random integers between 0 and 9 inclusive. Suppose the following results are obtained. Use a 0.05 significance level to test the claim that the computer generates digits
An observed frequency distribution is as follows: Number of successes 0 1 2 3 Frequency 89 133 52 26 a. Assuming a binomial distribution with n = 3 and p = 1/3, use the binomial probability
In a recent year, customers of Victoria Fridge and Stove (which is open 7 days a week) returned 146 appliances. If the frequencies of returns on different days conform to a Poisson distribution, they
An observed frequency distribution of sample IQ scores is as follows:a. Assuming a normal distribution with /A = 100 and Ïƒ = 15, use the methods given in Chapter 5 to find the probability
One of the authors observed 500 spins of the roulette wheel at the Mirage Resort and Casino. For each spin, the ball can land in any one of the 38 different slots that are supposed to be equally
Such measures of inflation as the consumer price index can also be used to compare prices in different regions. A standardized "basket" of grocery or consumer items can be purchased in different
A labour specialist is analyzing the numbers of work stoppages in the transportation industry. She claims that, in general, 10% of stoppages involve air transport, 10% involve rail transport, 20%
A study was made of 147 industrial accidents that required medical attention. Among those accidents, 31 occurred on Monday, 42 on Tuesday, 18 on Wednesday, 25 on Thursday, and 31 on Friday (based on
Use a 0.05 significance level and the industrial accident data from Exercise 6 to test the claim of a safety expert that accidents are distributed on workdays as follows: 30% on Monday, 15% on
The Gleason Supermarket's manager must decide how much of each ice cream flavour he should stock so that customer demands are satisfied but unwanted flavours don't result in waste. The ice-cream
The number TT is an irrational number with the property that when we try to express it in decimal form, it requires an infinite number of decimal places and there is no pattern of repetition. In the
Table 10-13 summarizes data for male survey subjects, but the accompanying table summarizes data for a sample of women. Using a 0.01 significance level, and assuming that the sample sizes of 800 men
A study of randomly selected car accidents and drivers who use cellular phones provided the following sample data. At the 0.05 level of significance, test the claim that the occurrence of accidents
A provider of uniforms for CFL players is examining players' weights. The accompanying table compares the weights of 32 randomly selected offensive backs (including quarterbacks) in the league. At
Winning team data were collected for teams in different sports, with the results given in the accompanying table. Use a 0.10 level of significance to test the claim that home/visitor wins are
The accompanying table lists sample data that statistician Karl Pearson used in 1909. Does the type of crime appear to be related to whether the criminal drinks or abstains? Are there any crimes that
A study of people who refused to answer survey questions provided the randomly selected sample data in the accompanying table. At the 0.01 significance level, test the claim that the cooperation of
Refer to Data Set 8 in Appendix B and test the claim that the gender of statistics students is independent of whether they smoke.
Refer to Data Set 8 in Appendix B and test the claim that whether statistics students exercise is independent of gender.
The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates' correction for continuity in cells with an expected frequency of
For a contingency table with two rows and two columns and frequencies of a and b in the first row and frequencies of c and d in the second row, verify that the test statistic becomesWhere and is
The number of overnight trips to Canada declined from 1996 to 1997, perhaps partly in response to the world financial conditions of 1997. Were these changes from year to year independent of the
Nicorette is a chewing gum designed to help people stop smoking cigarettes. Tests for adverse reactions yielded the results given in the accompanying table. At the 0.05 significance level, test the
Both proponents of and skeptics about health-store pills and nutritional supplements agree that to make valid claims about them, more clinical research on alternative medicines is necessary. One
Firms that sponsor or participate in sporting events to gain marketing exposure like to represent winning teams. The accompanying table shows the numbers of cars of different makes in the top 14 and
In a study of store checkout scanning systems, samples of purchases were used to compare the scanned prices to the posted prices. The accompanying table summarizes results for a sample of 819 items.
The Boeing Commercial Airplane Group conducted a survey of 133 planes being flown or on order from three airline companies based in different countries. The sample data are summarized in the
A market researcher investigated cars and trucks sold in Canada to determine whether the proportions of sales for these two vehicle types were the same for all manufacturers. He examined randomly
A sports-medicine clinic is investigating the relation between types of sports injuries and the ages of patients involved. The accompanying table summarizes randomly selected sample data for patients
In a survey at a mall during August, people were asked how much they spent that day. For a sample of 8 people, these were the results: 50 75 100 120 140 150 240 1350Are the sales normally
In the previous question, 1350 is an outlier. If we remove this value, show why the sales without outliers are normally distributed at a 0.05 level of significance.
A factory wanted to institute a quality control program. In theory, the diameter of a certain plastic part to be used in build-it-yourself furniture should be normally distributed with a mean of 15
Refer to the height data in Data Set 8. Use normal probability plots to confirm the assumption of normality. (Be sure to identify and remove the outlier in the data set-you can't miss it.)
In the x1 goodness-of-fit test, suppose the total number of observations is n. If the number of observations in each category is multiplied by a common factor N, show why the value of the test
The latest product of a cat food manufacturer is apparently well liked and nutritious, but cans are reportedly going bad before the end of their stated shelf life. Tests are now being conducted with
In recent years, El Nino phenomena have been popularly blamed for a variety of weather effects. The accompanying table compares the number of springs with precipitation levels at least 2% above
Based on seven years of data collected by Transport Canada, 72% of all bird strikes on moving aircraft involve gulls, sparrows, swallows, or snow buntings. The accompanying table is based on a random
Refer to Data Set 18 in Appendix B, which shows the body temperatures for people who were sufficiently healthy to be accepted for voluntary surgery. Below, the temperature ranges of females and males
Clinical tests of the allergy drug Seldane yielded results summarized in the accompanying table. At the 0.05 significance level, test the claim that the occurrence of headaches is independent of the
Assume that Table 10-15 lists test scores for four people, where the x score is from a test of memory and the y score is from a test of reasoning. Test the claim that both sets of scores are normally
Assume that Table 10-15 lists test scores for four people, where the x score is from a pretest taken before a training session on memory improvement and the y score is from a test taken after the
Assume that in Table 10-15, the letters A, B, C, and D represent the choices on the first question of a multiple-choice quiz. Also assume that x represents men and y represents women, and the table
Assume that in Table 10-15, the letters A, B, C, D represent different versions of the same test of reasoning. The x scores were obtained by four randomly selected men and the y scores were obtained
Assume that a sample of n pairs of data results in the given value of r. Is there is a significant linear correlation between x and y? Explain. a. n = 32, r = 0.992 b. n = 50, r = -0.333 C n = 17,
An investor, considering whether to add a mining stock to his portfolio as a long-term investment, compared, for the years 1995-2000, the year's closing price for a Toronto-based mining firm and the
To investigate the relationship between a person's education level and his or her salary, these variables were compared for people in selected occupations. Salaries are shown in thousands of dollars.
A stock-market investor is seeking clues to pick the most profitable companies. The accompanying table lists, for each of 11 companies, its profit margin (as a percent) versus its ratio of current
Refer to Data Set 16 in Appendix B. a. Use the paired data for durations and intervals after eruptions of the Old Faithful geyser. Is there a significant linear correlation, suggesting that the
Refer to Data Set 4 in Appendix B and use the paired columns for annual temperature and precipitation. Based on the result, does there appear to be a significant linear correlation between annual
Refer to Data Set 21 in Appendix B. a. Use the paired data consisting of price and carat (weight). Is there a significant linear correlation between the price of a diamond and its weight in
Refer to Date Set 4 in Appendix B and use the paired columns for annual temperature and snowfall. Based on the results, does there appear to be a significant correlation between annual temperature
Unlike Data Set 4, Data Set 7 in Appendix B records precipitation levels and temperatures in terms of deviations from seasonal norms, rather than in absolute terms. Use the columns in Data Set 7 in
The data on the next page are extracted from the top ten entries in the Financial Post list of top 500 companies. The number of employees is given in thousands and the revenues for 1997 are given in
Assume that a sample of n pairs of data results in the given value of r. Is there is a significant linear correlation between x and y? Explain. a. n = 22, r = -0.087 b. n = 40, r = 0.299 C. « = 25,
Given: There is a significant linear correlation between personal income and years of education. Conclusion: More education causes a person's income to rise.
Given: There is a significant linear correlation between provincial average tax burdens and provincial average incomes. Conclusion: There is a significant linear correlation between individual tax
How is the value of the linear correlation coefficient r affected in each of the following cases? a. Each x value is switched with the corresponding y value. b. Each x value is multiplied by the same

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