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introduction to probability statistics
Questions and Answers of
Introduction To Probability Statistics
12.57 Lobster The table gives the numbers of Octolasmis tridens and O. lowei barnacles on each of 10 lobsters." Does it appear that the barnacles compete for space on the surface of a lobster?a. If
12.56 Reverse the slope of the line in Exercise 12.55 by reordering the y observations, as follows:Repeat the steps of Exercise 12.55. Notice the change in the sign of r and the relationship between
12.55 You are given these data:a. Plot the six points on graph paper.b. Calculate the sample coefficient of correlation and interpret.c. By what percentage was the sum of squares of deviations
12.54 You are given these data:a. Plot the data points. Based on your graph, what will be the sign of the sample correlation coefficient?b. Calculate r and r and interpret their values. x -2 -1 0 1 2
12.53 What value does r assume if all the data points fall on the same straight line in these cases?a. The line has positive slope.b. The line has negative slope.
12.52 Describe the significance of the algebraic sign and the magnitude of r.
12.51 How does the coefficient of correlation measure the strength of the linear relationship between two variables y and x?
Refer to the height and weight data in Example 12.7. The correlation of height and weight was calculated to be r = 0.8261. Is this correlation significantly different from 0?
The heights and weights of n = 10 offensive backfield football players are randomly selected from a county's football all-stars. Calculate the correlation coefficient for the heights (in centimetres)
12.50 Drew Brees, continued Refer to Exercise 12.49.a. Estimate the average number of passing yards for games in which Brees throws 20 completed passes using a 95% confidence interval.b. Predict the
12.49 Drew Brees The number of passes completed and the total number of passing yards for Drew Brees, quarterback for the New Orleans Saints, were recorded for the 16 regular games in the 2010
12.48 Stride Rate, continued Refer to Exercise 12.47.a. Estimate the average stride rate if the speed is 5.8 metres per second using a 95% confidence interval.b. Predict the actual number of the
12.47 Stride Rate One measure of form for a runner is stride rate, defined as the number of steps per second. A runner is considered to be efficient if the stride rate is close to optimum. The stride
12.46 Strawberries III The following data (Exercises 12.18 and 12.28) were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage
12.45 Housing Prices II Refer to Exercise 12.44 and data set EX1244.a. Estimate the average increase in the price for an increase of 1 m for houses sold in the city. Use a 99% confidence interval.
12.44 Housing Prices If you try to rent an apartment or buy a house, you find that real estate representatives establish apartment rents and house prices on the basis of square footage of heated
12.43 What to Buy? A marketing research experiment was conducted to study the relationship between the length of time necessary for a buyer to reach a decision and the number of alternative package
12.42 Refer to Exercise 12.7. Portions of the MINITAB printout are shown here.a. Find a 95% confidence interval for the average value of y when x = 2.b. Find a 95% prediction interval for some value
12.41 Refer to Exercise 12.6.a. Estimate the average value of y when x = 1, using a 90% confidence interval.b. Find a 90% prediction interval for some value of y to be observed in the future when x =
Prior to fitting a line to the calculus grade-achievement score data, you may have thought that a score of 0 on the achievement test would predict a grade of 0 on the cal- culus test. This implies
A student took the achievement test and scored 50 but has not yet taken the calculus test. Using the information in Example 12.1, predict the calculus grade for this student with a 95% prediction
Use the information in Example 12.1 to estimate the average calculus grade for students whose achievement score is 50, with a 95% confidence interval.
12.40 LCD TVs As technology improves, the choice of televisions becomes more compli- cated. Should you choose an LCD TV, an LED TV, or a plasma TV? Does the price of an LCD TV depend on the size of
12.39 Systolic Blood Pressure (SBP) and Body Mass Index (BMI), again Refer to Exercise 12.29. The MINITAB printout is reproduced here.a. What assumptions must be made about the distribution of the
12.38 Professor Asimov, again Refer to Exercise 12.9, in which the number of books x written by Isaac Asimov are related to the number of months y he took to write them. A plot of the data is
12.37 Air Pollution Refer to Exercise 12.23, in which an air pollution monitor's response to ozone was recorded for several different concentrations of ozone. Use the MINITAB residual plots to
12.36 Chirping Crickets Refer to Exercise 12.24, in which the number of chirps per second for a cricket was recorded at 10 different temperatures. Use the MINITAB diagnostic plots to comment on the
12.35 Refer to the data in Exercise 12.7. The normal probability plot and the residuals versus fitted values plots generated by MINITAB are shown here. Does it appear that any regression assumptions
12.34 What diagnostic plot can you use to determine whether the assumption of equal variance has been violated? What should the plot look like when the variances are equal for all values of x?
12.33 What diagnostic plot can you use to determine whether the incorrect model has been used? What should the plot look like if the correct model has been used?
12.32 What diagnostic plot can you use to determine whether the data satisfy the normality assumption? What should the plot look like for normal residuals?
12.31 Armspan and Height II In Exercise 12.17 (data set EX1217), we measured the armspan and height of eight people with the following results:a. Does the data provide sufficient evidence to indicate
12.30 Systolic Blood Pressure (SBP) and Body Mass Index (BMI), continued Refer to Exercise 12.29.a. Use the MINITAB printout to find the value of the coefficient of determination, 2. Show that P =
12.29 Systolic Blood Pressure (SBP) and Body Mass Index (BMI) In the case study of Chapter 1 we provided the blood pressure data on 500 persons (both male and females). Here we take a random sample
12.28 Strawberries II The following data (Exercise 12.18 and data set EX1218) were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage
12.27 Sleep Deprivation III Refer to the sleep deprivation experiment described in Exercise 12.11 and data set EX1211. The data and the MINITAB and Excel printouts are reproduced here.a. Do the data
12.26 Professor Asimov, continued Refer to the data in Exercise 12.9, relating x, the number of books written by Professor Isaac Asimov, to y, the number of months he took to write his books (in
12.25 Gestation Times and Longevity The table below shows the gestation time in days and the average longevity in years for a variety of mammals in captivity.a. If you want to estimate the average
12.24 Cricket (the insect, not the game) Crickets make their chirping sounds by rapidly sliding one wing over the other. The faster they move their wings, the higher the chirping sound that is
12.23 Air Pollution An experiment was designed to compare several different types of air pollution monitors.4 The monitor was set up, and then exposed to different concentrations of ozone, ranging
12.22 Refer to Exercise 12.8. The data, along with the Excel analysis of variance table, are reproduced below:a. Do the data provide sufficient evidence to indicate that y and x are linearly related?
12.21 Refer to Exercise 12.7. The data, along with the MINITAB analysis of variance table, are reproduced below.a. Do the data provide sufficient evidence to indicate that y and x are linearly
12.20 Refer to Exercise 12.19. Find a 95% confi- dence interval for the slope of the line. What does the phrase "95% confident" mean?
12.19 Refer to Exercise 12.6. The data are reproduced below.a. Do the data present sufficient evidence to indicate that y and x are linearly related? Test the hypothesis that =0 at the 5% level of
Find a 95% confidence interval estimate of the slope for the calculus grade data in Table 12.1. TABLE 12.1 Mathematics Achievement Test Scores and Final Calculus Grade for Grade 12 Students from
Determine whether there is a significant linear relationship between the calculus grades and test scores listed in Table 12.1. Test at the 5% level of significance. TABLE 12.1 Mathematics Achievement
12.18 Strawberries The following data were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage temperature).a. Find the least-squares line
12.17 Armspan and Height Leonardo daVinci (1452-1519) drew a sketch of a man, indicating that a person's armspan (measuring across the back with your arms outstretched to make a "t") is roughly equal
12.16 Test Interviews, continued Refer to Exercise 12.15. Construct the ANOVA table for the linear regression relating y, the score on Test 2, to x, the score on Test 1.
12.15 Test Interviews Of two personnel evaluation techniques available, the first requires a two-hour test interview, while the second can be completed in less than an hour. The scores for each of
12.14 How Long Is It? How good are you at estimating? To test a subject's ability to estimate sizes, he was shown 10 different objects and asked to estimate their length or diameter. The object was
12.13 Global Warming? The following table shows annual mean global surface temperature anomaly for the period 1972 to 2001 provided by the Global Historical Climate Network (GHCN).a. Which of the two
12.12 Sleep Deprivation II Refer to the data given in the sleep deprivation experiment in Exercise 12.11. Answer the questions posed in partsa, b,d, and e of that exercise by completing the following
12.11 Sleep Deprivation A study was conducted to determine the effects of sleep deprivation on people's ability to solve problems without sleep. A total of 10 subjects participated in the study, two
12.10 A Chemical Experiment Using a chemical procedure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given
12.9 Professor Asimov Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career
12.7 Six points have these coordinates:a. Find the least-squares line for the data.b. Plot the six points and graph the line. Does the line appear to provide a good fit to the data points?c. Use the
12.5 What is the difference between deterministic and probabilistic mathematical models?
12.4 Give the equation and graph for a line with y-intercept equal to -3 and slope equal to 1.
12.3 Give the equation and graph for a line with y-intercept equal to 3 and slope equal to -1.
12.1 Graph the line corresponding to the equation y=2x+1 by graphing the points corresponding to x = 0, 1, and 2. Give the y-intercept and slope for the line.
Find the least-squares prediction line for the calculus grade data in Table 12.1. TABLE 12.1 Mathematics Achievement Test Scores and Final Calculus Grade for Grade 12 Students from High School
13.27 Advertising and Sales, continued Refer to Exercise 13.26. Use a computer software package to perform the multiple regression analysis and obtain diagnostic plots if possible.a. Comment on the
Suppose that a response variable Y is related to four predictor variables, X1, X2, X3, and x4, so that k = 4. 1. Enter the observed values of y and each of the k = 4 predictor variables into the
Suppose that a response variable Y is related to four predictor variables, x1, x2, x3, and x4, so that k = 4. 1. Enter the observed values of y and each of the k = 4 predictor variables into the
Refer to the real estate data of Example 13.2 that relate the listed selling price y to the square metres of living area x, the number of floors x2, the number of bedrooms X3, and the number of
13.19 A multiple linear regression model involv- ing one qualitative and one quantitative independent variable produced this prediction equation: y= 12.6+0.54x1-1.2x1x2 + 3.9xa. Which of the two
13.18 Suppose E(Y) is related to two predictor variables x and x2 by the equation E(Y) 3+x 2x2 + x1x2a. Graph the relationship between E(Y) and x, when x20. Repeat for x2 = 2 and for x2 = -2.b.
13.17 Production Yield Suppose you wish to predict production yield y as a function of several independent predictor variables. Indicate whether each of the following independent variables is
Refer to Example 13.6. Do the data provide sufficient evidence to indicate that the annual rate of increase in male junior faculty salaries exceeds the annual rate of in- crease in female junior
A study was conducted to examine the relationship between university salary Y, the number of years of experience of the faculty member, and the gender of the faculty member. If you expect a
13.11 University Textbooks II Refer to Exercise 13.10.a. Use the values of SSR and Total SS to calculate R. Compare this value with the value given in the printout.b. Calculate R(adj). When would it
13.8 Refer to Exercise 13.5.a. Suppose that the relationship between E(Y) and x is a straight line. What would you know about the value of B?b. Do the data provide sufficient evidence to indicate
13.7 Refer to Exercise 13.5.a. What is your estimate of the average value of y when x = 0?b. Do the data provide sufficient evidence to indicate that the average value of y differs from 0 when x = 0?
13.6 Refer to Exercise 13.5.a. What is the prediction equation?b. Graph the prediction equation over the interval 0 x 6.
13.3 Suppose that you fit the model E(Y) Bo+Bx + B2x2 + B3x3 to 15 data points and found F equal to 57.44.a. Do the data provide sufficient evidence to indicate that the model contributes information
13.2 Refer to Exercise 13.1.a. Graph the relationship between E(Y) and x2 when x=0. Repeat for x = 1 and for x = 2.b. What relationship do the lines in part a have to one another?c. Suppose, in a
13.1 Suppose that E(Y) is related to two predictor variables, X, and X2, by the equation E(Y)=3+x1-2x2a. Graph the relationship between E(Y) and x, when x2 = 2. Repeat for x2 = 1 and for x2 = 0.b.
Refer to the data on grocery retail outlet productivity and outlet size in Example 13.3. MINITAB was used to fit a quadratic model to the data and to graph the quadratic predic- tion curve, along
Suppose you want to relate a random variable Y to two independent variables x and x2. The multiple regression model is Y=Bo+B1x+B2x2 + with the mean value of y given as E(Y) Bo+B+ Bx2
11.39 Slash Pine Seedings An experiment was conducted to determine the effects of three methods of soil preparation on the first-year growth of slash pine seedlings. Four locations (provincial forest
11.50 Animation Helps? To explore ways to increase the educational experience using animation versus static images in a learning environment, Cyril Rebetez and colleagues ran a factorial experiment
11.51 Standardized Test Scores A local school board was interested in comparing test scores on a standarized reading test for Grade 3 students in its district. It selected a random sample of five
11.52 Management Training An experiment was conducted to investigate the effect of manage- ment training on the decision-making abilities of supervisors in a large corporation. Sixteen supervi- sors
11.53 Management Training, continued Refer to Exercise 11.52. The data for this experiment are shown in the table.a. Construct the ANOVA table for this experiment.b. Is there a significant
The data from Example 11.4 involving breakfast and the attention spans of three groups of elementary students were analyzed using MINITAB. The graphs in Figure 11.12, gen- erated by MINITAB, are the
A company plans to promote a new product by using one of three advertising cam- paigns. To investigate the extent of product recognition from these three campaigns, 15 market areas were selected and
Completely Randomized Design Refer to the breakfast study in Example 11.4, in which the effect of nutrition on attention span (in minutes) was studied.1. Enter the data into columns A, B, and C of an
Randomized Block Design Refer to the cell phone study in Example 11.9, in which the effect of usage level on cost (in dollars) was studied for four different companies. 1. Enter the data into
11.54 Reaction Times vs. Stimuli Twenty-seven people participated in an experi- ment to compare the effects of five different stimuli on reaction time. The experiment was run using a com- pletely
11.55 Refer to Exercise 11.54. Use this MINITAB output to identify the differences in the treatment means. MINITAB output for Exercise 11.55 Tukey 95 Simultaneous Confidence Intervals All Pairwise
11.49 The Cost of Flying In an attempt to determine what factors affect airfares, a researcher recorded a weighted average of the costs per kilometre for two airports in each of three major U.S.
11.48 Terrain Visualization A study was con- ducted to determine the effect of two factors on terrain visualization training for soldiers. During the training programs, participants viewed contour
11.40 Digitalis and Calcium Uptake A study was conducted to compare the effects of three levels of digitalis on the levels of calcium in the heart muscles of dogs. Because general level of calcium
11.41 Bidding on Construction Jobs A building contractor employs three construction engineers, A, B, and C, to estimate and bid on jobs. To determine whether one tends to be a more conservative (or
Suppose that the two supervisors are each observed on three randomly selected days for each of the three different shifts. The average outputs for the three shifts are shown in Table 11.4 for each of
Table 11.6 shows the original data used to generate Table 11.5 in Example 11.12. That is, the two supervisors were each observed on three randomly selected days for each of the three different
11.43 The analysis of variance table for a 34 factorial experiment, with factor A at three levels and factor B at four levels, and with two observations per treatment, is shown here:a. Fill in the
11.44 Refer to Exercise 11.43. The means of two of the factor-level combinations-say, AB and A2B are =8.3 and x2 = 6.3, respectively. Find a 95% confidence interval for the difference between the two
11.45 The table gives data for a 3 x 3 factorial experiment, with two replications per treatment:a. Perform an analysis of variance for the data, and present the results in an analysis of variance
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