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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

15.31 Images and Word Recall A psychol- ogy class performed an experiment to determine whether a recall score in which instructions to form images of 25 words were given differs from an initial
The data in Table 15.9 were collected using a completely randomized design. They are the achievement test scores for four different groups of students, each group taught by a different teaching
Compare the results of the analysis of variance F test and the Kruskal-Wallis H test for testing for differences in the distributions of achievement test scores for the four teaching techniques in
15.32 Three treatments were compared using a completely randomized design. The data are shown in the table.Do the data provide sufficient evidence to indicate a difference in location for at least
15.33 Four treatments were compared using a completely randomized design. The data are shown here:Do the data provide sufficient evidence to indicate a difference in location for at least two of the
15.34 Swampy Sites II Exercise 11.13 presents data (see data set EX1113) on the rates of growth of vegetation at four swampy underdeveloped sites. Six plants were randomly selected at each of the
15.35 Heart Rate and Exercise Exercise 11.58 presented data (data set EX1158) on the heart rates for samples of 10 men randomly selected from each of four age groups. Each man walked a treadmill at a
15.36 pH Levels in Water A sampling of the acidity of rain for 10 randomly selected rainfalls was recorded at three different locations in Canada: The prairies, the Atlantic region, and the West
15.37 Advertising Campaigns The results of an experiment to investigate product recognition for three advertising campaigns were reported in Example 11.15. The responses were the percentage of 400
Suppose you wish to compare the reaction times of people exposed to six different stimuli. A reaction time measurement is obtained by subjecting a person to a stimulus and then measuring the time
Find the approximate p-value for the test in Example 15.8.
15.39 A randomized block design is used to compare four treatments in eight blocks.a. Use the Friedman F, test to detect differences in location among the four treatment distributions. Test using a =
15.40 Supermarket Prices In a comparison of the prices of items at five supermarkets, six items were randomly selected and the price of each was recorded for each of the five supermarkets. The
15.41 Toxic Chemicals An experiment was EX1541 conducted to compare the effects of three toxic chemicals, A, B, and C, on the skin of rats. One- centimetre squares of skin were treated with the
15.42 Good Tasting Medicine In a study of the palatability of antibiotics in children, Dr. Doreen Matsui and colleagues used a voluntary sample of healthy children to assess their reactions to the
Calculate r, for the data in Table 15.12. TABLE 15.12 Test Rank, y Ranks of Data in Table 15.11 Teacher 1 Judge's Rank, x; 7 2 3 4 5 7 8 66900 1 5 3 48726 4261385
Test the hypothesis of no association between the populations for Example 15.10.
15.43 Give the rejection region for a test to detect positive rank correlation if the number of pairs of ranks is 16 and you have these a-values:a. a 0.05 =b. a = 0.01
15.44 Give the rejection region for a test to detect negative rank correlation if the number of pairs of ranks is 12 and you have these a-values:a. a 0.05b. a = 0.01 =
15.45 Give the rejection region for a test to detect rank correlation if the number of pairs of ranks is 25 and you have these a-values:a. = 0.05 ab. = 0.01
15.46 The following paired observations were obtained on two variables x and y:a. Calculate Spearman's rank correlation coefficient r..b. Do the data present sufficient evidence to indicate a
15.47 Rating Political Candidates A political scientist wished to examine the relationship between the voter image of a conservative political candidate and the distance (in kilometres) between the
15.48 Competitive Running Is the number of years of competitive running experience related to a runner's distance running performance? The data on nine runners, obtained from the study by Scott
15.49 Tennis Racquets The data shown in the accompanying table give measures of bending stiffness and twisting stiffness as determined by engineering tests on 12 tennis racquets.a. Calculate the rank
15.50 Student Ratings A school principal suspected that a teacher's attitude toward a Grade 1 student depended on his original judgment of the child's ability. The principal also suspected that much
15.51 Student Ratings, continued Refer to Exercise 15.50. Do the data provide sufficient evidence to indicate a positive correlation between the teacher's ranks and the ranks of the IQs? Use a =
15.52 Art Critics Two art critics each ranked 10 paintings by contemporary (but anonymous) artists in accordance with their appeal to the respective critics. The ratings are shown in the table. Do
15.53 Rating Tobacco Leaves An experiment was conducted to study the relationship between the ratings of a tobacco leaf grader and the moisture content of the tobacco leaves. Twelve leaves were rated
15.54 Social Skills Training A social skills training program was implemented with seven mildly challenged students in a study to determine whether the program caused improvements in pre/post
15.55 Response Times An experiment was conducted to compare the response times for two different stimuli. To remove natural person-to- person variability in the responses, both stimuli were presented
15.56 Response Times, continued Refer to Exercise 15.55. Test the hypothesis that no difference exists in the distributions of response times for the two stimuli, using the Wilcoxon signed-rank test.
15.57 Identical Twins To compare two EX1557 middle schools, A and B, in academic effectiveness, an experiment was designed requiring the use of 10 sets of identical twins, each twin having just
15.58 Identical Twins II Refer to Exercise 15.57. What answers are obtained if Wilcoxon's signed-rank test is used in analyzing the data? Compare with your earlier answers.
15.59 Paper Brightness The coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are given in the table for samples of nine observations drawn
15.60 Precision Instruments Assume (as in the case of measurements produced by two well-calibrated measuring instruments) the means of two populations are equal. Use the Wilcoxon rank sum statistic
15.61 Meat Tenderizers An experiment was conducted to compare the tenderness of meat cuts treated with two different meat tenderizers, A and B. To reduce the effect of extraneous variables, the data
15.62 Interviewing Job Prospects A large corporation selects university graduates for employment using both interviews and a psychological achievement test. Interviews conducted at the home office of
15.63 Interviews, continued Refer to Exercise 15.62. Do the data present sufficient evidence to indicate that the correlation between interview rankings and test scores is less than 0? If this
15.64 Word Association Experiments A comparison of reaction times for two different stimuli in a psychological word-association experiment produced the accompanying results when applied to a random
15.65 Math and Art The table gives the scores of a group of 15 students in mathematics and art. Use Wilcoxon's signed-rank test to determine whether the median scores for these students differ
15.66 Math and Art, continued Refer to Exercise 15.65. Compute Spearman's rank correlation coefficient for these data and test Ho: no association between the rank pairs at the 10% level of
15.67 Yield of Wheat Exercise 11.66 presented an analysis of variance of the yields of five different vari- eties of wheat, observed on one plot each at each of six different locations (see data set
15.68 Learning to Sell In Exercise 11.59, you compared the numbers of sales per trainee after completion of one of four different sales training programs (sec data set EX1159). Six trainees completed
15.69 Pollution from Chemical Plants In Exercise 11.64, you performed an analysis of variance to compare the mean levels of effluents in water at four different industrial plants (see data set
15.70 AIDS Research Scientists have shown that a newly developed vaccine can shield rhesus monkeys from infection by a virus closely related to the AIDS-causing human immunodeficiency virus (HIV). In
15.71 Heavy Metal An experiment was performed to determine whether there is an accumulation of heavy metals in plants that were grown in soils amended with sludge and whether there is an accumulation
15.72 Refer to Exercise 15.71. The data in this table are the cadmium concentrations found in aphids that fed on the plants grown in soil amended with sludge.a. Use the MINITAB normal probability
15.73 Rating Teaching Applicants Before filling several new teaching positions at the high school, the principal formed a review board consisting of five teachers who were asked to interview the 12
15.74 Contaminants in Chemicals A man- ufacturer uses a large amount of a certain chem- ical. Since there are just two suppliers of this chemical, the manufacturer wishes to test whether the
15.75 Lighting in the Classroom The productivity of 35 students was observed and measured both before and after the installation of new lighting in their classroom. The productivity of 21 of the 35
15.76 Reducing Cholesterol A drug was developed for reducing cholesterol levels in heart patients. The cholesterol levels before and after drug treatment were obtained for a random sample of 25 heart
15.77 Legos The time required for kindergarten children to assemble a specific Lego creation was measured for children who had been instructed for four different lengths of time. Four children were
15.78 Worker Fatigue To investigate methods of reducing fatigue among employees whose jobs involve a monotonous assembly procedure, 12 randomly selected employees were asked to perform their usual
15.79 Ranking Cricket Batsmen A ranking of the batsmen in the top eight teams in the world was made by polling a number of professional coaches and sportswriters. This "true ranking" is shown below,
1. What type of design has been used in this taste-testing experiment?As consumers become more and more interested in eating healthy foods, many "light," "fat-free," and "cholesterol-free" products
2. Do the data satisfy the assumptions required for a parametric analysis of variance? Explain.As consumers become more and more interested in eating healthy foods, many "light," "fat-free," and
3. Use the appropriate nonparametric technique to determine whether there is a signifi- cant difference between the average scores for the three brands of egg substitutes.As consumers become more and
A report published in the International Journal of Obesity claims the "biggie size" fries and lack of exercise aren't the only factors to blame for North America's battle of the bulge. Researchers
Having the appropriate amount of water will increase or boost metabolism and reg- ulate body temperature. The basal metabolism of ten females was examined and recorded before and after drinking the
You can increase your BMR by implementing one of the following strategies: Strategy 1: Having the appropriate amount of water will increase or boost metabolism and regulate body temperature. Strategy
A researcher designs an experiment in which a rat is attracted to the end of a ramp that divides, leading to doors of three different colours. The researcher sends the rat down the ramp n = 90 times
Statistics Canada reported that in the proportions of Canadian university teachers/ professors by religion. According to Statistics Canada, the proportion of Roman Catholic (R), Christian (C), no
14.5 Suppose that a response can fall into one of k = 5 categories with probabilities P1, P2, ... Ps and that n = 300 responses produced these category counts:a. Are the five categories equally
14.6 Suppose that a response can fall into one of k = 3 categories with probabilities p = 0.4, P2 = 0.3, and p = 0.3, and n = 300 responses produce these category counts:Do the data provide
14.7 Your Favourite Lane A highway with four lanes in each direction was studied to see whether drivers prefer to drive on the inside lanes. A total of 1000 automobiles were observed during heavy
14.9 Heart Attacks on Mondays Do you hate Mondays? Researchers from Germany have provided another reason for you: They concluded that the risk of a heart attack for a working person may be as much as
14.10 Mortality Statistics Medical statistics show that deaths due to four major diseases-call them A, B, C, and D account for 15%, 21%, 18%, and 14%, respectively, of all non-accidental deaths. A
14.11 Schizophrenia Research has suggested a link between the prevalence of schizophrenia and birth during particular months of the year in which viral infections are prevalent. Suppose you are work-
14.13 M&Ms The Mars, Inc. website reports the fol- lowing percentages of the various colours of its M&M candies for the "milk chocolate" variety:A 400-gram bag of milk chocolate M&Ms is
14.14 Peanut M&Ms The percentage of various colours are different for the "peanut" variety of Mars M&M candies, as reported on the Mars, Inc. website:A 400-gram bag of peanut M&Ms is
A total of n = 309 furniture defects were recorded and the defects were classified into four types: A, B, C, or D. At the same time, each piece of furniture was identified by the production shift in
A survey was conducted to evaluate the effectiveness of a new flu vaccine that had been administered in a small community. The vaccine was provided free of charge in a two-shot sequence over a period
14.16 Calculate the value and give the number of degrees of freedom for x for these contingency tables: a. Columns Rows 1 2 3 4 1 120 70 55 16 23 2 79 108 95 43 31 49 81 140 b. Rows 1 Columns 1 2 3 1
14.18 A survey of 400 respondents produced these cell counts in a 2 3 contingency table:a. If you wish to test the null hypothesis of "independence" that the probability that a response falls in any
14.19 Gender Differences Male and female respondents to a questionnaire on gender differences were categorized into three groups according to their answers on the first question:Use the MINITAB
14.20 Same-Sex Legislation Do you think the next government should let same-sex legislation stand or should it repeal? In 2005 The Strategic Counsel, on behalf of the Globe and Mail/CTV polling
14.21 Anxious Infants A study was conducted by Joseph Jacobson and Diane Wille to determine the effect of early child care on infant-mother attachment patterns. In the study, 93 infants were
14.22 Spending Patterns Is there a difference in the spending patterns of grade 12 students depending on their gender? A study to investigate this question focused on 196 employed grade 12 students.
14.23 Waiting for a Prescription How long do you wait to have your prescriptions filled? According to a survey, "about 3 in 10 Canadians wait more than 20 minutes to have a prescription filled."
14.24 The JFK Assassination On the fortieth anniversary of JFK's assassination, a FOX News poll showed most Americans disagree with the government's conclusions about the killing. The Warren
14.25 Telecommuting As an alternative to flextime, many companies allow employees to do some of their work at home. Individuals in a random sample of 300 workers were classified according to salary
14.26 Telecommuting II An article addressed the same telecommuting issue (Exercise 14.25) in a slightly different way. It concluded that "people who work exclusively at home tend to be older and
In another flu prevention experiment like the one described in Example 14.5, the ex- perimenter decides to search the clinic records for 300 patients in each of the three treatment categories: no
A survey of voter sentiment was conducted in four midcity political wards to compare the fractions of voters who favour candidate A. Random samples of 200 voters were polled in each of the four wards
14.27 Random samples of 200 observations were selected from each of three populations, and each observation was classified according to whether it fell into one of three mutually exclusive
14.29 Overweight Young Canadians The Canadian Community Health Survey of 2004 deals with overweight/obesity rates by ethnic origin among children aged 2 to 17 (excluding territories). Suppose the
14.30 Diseased Chickens A particular poultry dis- ease is thought to be non-communicable. To test this theory, 30,000 chickens were randomly partitioned into three groups of 10,000. One group had no
14.31 Wealth and Education Levels Does education really make a difference in how much money you will earn? Researchers randomly selected 100 people from each of three income categories "marginally
14.32 Deep-Sea Research W.W. Menard has conducted research involving manganese nodules, a mineral-rich concoction found abundantly on the deep- sea floor. In one portion of his report, Menard
14.33 How Big Is the Household? A local chamber of commerce surveyed 120 house- holds in its city-40 in each of three types of residence (apartment, duplex, or single residence) and recorded the
14.34 Birth Control versus Abor- tion Mexican adults remain opposed to pregnancy termination, according to a poll conducted by Consulta Mitofsky. Only 32.1% of respondents agree with abortion.
14.35 Evolution: Pro or Con? According to a poll by the Pew Research Center, 55% of young adults (ages 18-29) believe that evolution is the best explanation for the development of human life." When
Suppose you have recorded the gender (M or F) and the university status (1Y, 2Y, 3Y, 4Y, Grad) for 100 statistics students, as shown in the table below.1. Enter the observed values into the first
14.36 Floor Polish A manufacturer of floor pol- ish conducted a consumer preference experiment to see whether a new floor polish A was superior to those produced by four competitors, B, C, D, and E.
14.37 Physical Fitness in Canada A survey was conducted to investigate the interest of middle-aged adults in physical fitness programs in British Colum- bia, Alberta, Ontario, and Quebec. The
14.38 Fatal Accidents Accident data were analyzed to determine the numbers of fatal accidents for automo- biles of three sizes. The data for 346 accidents are as follows:Do the data indicate that the
14.39 Life under the EU Angus Reid Global Monitor reported that many adults in Britain and France are disappointed with the effect of the European Union (EU) in their countries, according to a poll
14.40 Discovery-based Teaching Two biology instructors set out to evaluate the effects of discovery-based teaching compared to the standard lecture-based teaching approach in the laboratory. 13 The
14.41 Flower Colour and Shape A botanist per- forms a secondary cross of petunias involving indepen- dent factors that control leaf shape and flower colour, where the factor A represents red colour,
14.42 Salmonella Is your holiday turkey safe? A federal survey found that 19.6% of turkeys are contam- inated with the salmonella bacteria. 14 Use the table that follows to determine if there is a

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