Question: Graph the straight line for the means
Graph the straight line for the means of the linear regression model 
having β0 = 3, β1 = -2.
> Using the data from Exercise 14.1, test for equality of means using a = .05. Data from Exercise 14.1: A group of eight students want to compare the quality of food at 4 campus area restaurants. The two students randomly assigned to a site, dine on diff
> Based on the current General Social Survey, an index is created from the few questions asking about the degree of confidence in government. Six age groups are compared. Suppose the values of the index result in the following ANOVA table. Carry out the F
> A psychologist investigating the connection between music and memory, randomly assigns subjects to one of three treatment groups. The first group hears white noise, the second Mozart, and the third heavy metal. With the appropriate background sound turne
> A group of eight students want to compare the quality of food at 4 campus area restaurants. The two students randomly assigned to a site, dine on different nights. Each student rates the quality of their meal on a ten point scale. Calling the restaurant
> (a) By expanding the square on the right-hand side of show that the x2 statistic can also be expressed as (b) Express the x2 statistic as where P^i = ni / n is the observed relative frequency. Note that doubling the sample size, while maintaining the sam
> Observations of 80 litters, each containing 3 rabbits, reveal the following frequency distribution of the number of male rabbits per litter. Under the model of Bernoulli trials for the sex of rabbits, the probability distribution of the number of males p
> Loss of calcium is a serious problem for older women. To investigate the amount of loss, a researcher measured the initial amount of bone mineral content in the radius bone of the dominant hand of elderly women and then the amount remaining after one yea
> Internet consumer ratings of the previous model smart speaker, based on ab out 100,000 ratings, can be summarized as: The ratings of the new model by 200 persons yielded the following frequency table. Do these data show a significantly different distribu
> Cross-fertilizing a pure strain of red flowers with a pure strain of white flowers produces pink hybrids that have one gene of each type. Crossing these hybrids can lead to any one of four possible gene pairs. Under Mendel's theory, these four are equall
> A shipment of assorted nuts is labeled as having 45% walnuts, 20% hazelnuts, 20% almonds, and 15% pistachios. By randomly picking several scoops of nuts from this shipment, an inspector finds the counts shown. Could these findings be a strong basis for a
> A market researcher wishes to assess consumers' preference among three different colors available on name-brand dishwashers. The following frequencies were observed from a random sample of 150 recent sales. Test the null hypothesis, at a = .05, that all
> Referring to the data in Exercise 13.2, test the null hypothesis that the probability of the blood types 0, A , B, and AB is in the ratios 4 :4 : l:l. Use  = .05. Data from Exercise 13.2: Recorded here is the frequency distribution of
> Do Exercise 13.24 on a computer. Data from Exercise 13.24: Out of 120 members of a club who responded to a survey, 80 said that the golfing facilities were influential, 53 said the dining facilities were influential, and 25 said both were influential in
> The analysis of a contingency table becomes tedious especially when the size of the table is large. Using a computer makes the task quite easy. The output is as follows: (a) Compare this output with the calculations. (b) Do Exercise 13.23 on a computer.
> Out of 120 members of a club who responded to a survey, 80 said that the golfing facilities were influential, 53 said the dining facilities were influential, and 25 said both were influential in their decision to join the club. (a) Construct a two-way t
> Lying can have major economic and social implications. A double blind trial was conducted to study the effect of testosterone on lying. Among 9 1 healthy men, n 1 = 46 received 50 mg of testosterone on a skin patch while the control group, n2 = 45, recei
> Refer to the mattress data in the chapter opener. (a) Can the observed differences be explained by chance or are mattress type and satisfaction level associated? (b) Determine the contribution of each cell to the x2 statistic. (c) For each cell, deter
> Old Faithful, the most famous geyser in Yellowstone Park, had the following durations (measured in seconds) in six consecutive eruptions: 240 248 113 268 117 253 (a) Find the sample median. (b) Find the sample mean.
> Th e article What Makes a Great Tweet concludes that only 36% of tweets are worth reading. A total of 4,220 tweets were rated in this study. Identify a statistical population and the sample.
> A consultant to all kinds of retailers suggests that they have plenty of baskets available for customers. He bases his suggestion on data collected by watching videos from hidden cameras. Suppose that out of 200 customers, 80 picked up a basket when they
> Applicants for public assistance are allowed an appeals process when they feel unfairly treated. At such a hearing, the applicant may choose self-representation or representation by an attorney. The appeal may result in an increase, decrease, or no chang
> Recorded here is the frequency distribution of the blood types of 100 persons who have volunteered to donate blood at a plasm a center. Test the goodness of fit of the model, which assumes that the four blood types are equally likely in the population of
> With reference to the sleep data in Table D. l 0 of the Data Bank, make two categories of snorers on the basis of the last variable: those who responded three or more times a week so their score is coded 4 or 5 and those who responded less than three tim
> Using the computer. The analysis of a contingency table can be conveniently done on a computer. For an illustration, we present here a MINITAB analysis of the data in Table 6, Example 5. The output is as follows: (a) Compare this output with the calculat
> Osteoporosis, or a loss of bone minerals, is a common cause of broken bones in the elderly. A researcher on aging conjectures that bone mineral loss can be reduced by regular physical therapy or certain kinds of physical activity. A study is conducted on
> Referring to Exercise 13.10, compare the conclusions of the level a = .OS (a) x2 test of homogeneity. (b) Z test that sales are higher with the modified page. Data from Exercise 13.10: A strategy called A/B testing is being implemented by many e-comme
> Using only the two conditions "signature at the top" and "no signature required, " (a) Make a 2 X 2 table and test H0 : PT = PN versus H1 : PT < PN at a = .02. (b) Obtain a 95% confidence interval for PN - PT·
> Using only the two conditions "signature at bottom" after filling out the form and "no signature required." (a) Conduct a x2 test. Take a = .05. (b) Does the conclusion of your test prove that the two probabilities PN and p8 are equal? Clearly explain t
> Referring to Exercise 3.10, double all of the counts. (a) Calculate the x2 statistic. (b) Compare your answer in Part a to the answer in Exercise 13.10 Data from Exercise 13.10: A strategy called A/B testing is being implemented by many e-commerce fir
> With reference to the number of returns, obtain the sample (a) mean and (b) median.
> Nausea from air sickness affects some travelers. In a comparative study of the effectiveness of two brands of motion sickness pills, brand A pills were given to 45 persons randomly selected from a group of 90 air travelers, while the other 45 persons wer
> Do Exercise 13.10 using computer software. Data from Exercise 13.10: A strategy called A/B testing is being implemented by many e-commerce firms. A product web page is modified by adding a picture or other visual change. Then, a fraction of the traffic
> A strategy called A/B testing is being implemented by many e-commerce firms. A product web page is modified by adding a picture or other visual change. Then, a fraction of the traffic is routed to the new page. For a sample of 1000 consumers who visit th
> Given below are the frequencies observed from 320 tosses of a die. Do these data cast doubt on the fairness of the die?
> Given the data, (a) Fit a quadratic curve using the equations. (b) Verify your answers using software.
> Referring to your answer to 12.7 p art 6, (a) Find a 95% confidence interval for βj . (b) Test H0 :p2 = 4 versus H1 :p2 > 4 with  = .05. Data from Exercise 12.7: Consider the data on a response variable and two predic
> Consider the data on a response variable and two predictor variables. (a) Fit a multiple regression model with response variable y. Note that the equations in the middle of page 391 simplify for these data. (b) Verify your answer using software.
> Consider the multiple linear regression model where βo = 2, β1, = -3, β2 = 2, and the normal random variable e h as standard deviation 3 . What is the mean of the response Y when x1 = 3 and x2 = - 2?
> In an experiment ( courtesy of W. Burkholder) involving stored-product beetles (Trogoderma glabrum) and their sex-attractant pheromone, the pheromone is placed in a pit-trap in the centers of identical square arenas. Marked beetles are then released alon
> An experiment was conducted for the purpose of studying the effect of temperature on the life length of an electrical insulation. Specimens of the insulation were tested under fixed temperatures, and their times to failure recorded. (a) Fit a straight li
> With reference to the extracurricular activities data in Exercise 2.3, obtain the (a) Sample mean. (b) Sample median. (c) Comment on the effect of a few large observations. Data from Exercise 2.3: A student at the University of Wisconsin surveyed 40
> Referring to Example 1, Table 1, three additional trials are now available. (a) Fit a straight line model with the square root of stopping distance as the response variable. (b) Find the proportion of variation explained by x. (c) Verify your answer to
> Refer to the data of Exercise 12.1. (a) Consider the reciprocal transformation y' = 1 / y and plot the scatter diagram of y' versus x. (b) Fit a straight line regression to the transformed data. (c) Calculate r 2 and comment on the adequacy of the fit.
> Referring to Exercise 12 .11 , we have added one more predictor x3 = skull width (cm). The output for a regression analysis. (a) Test H0 : β3 = 0 versus H0 : β3 ≠ 0 with = .05. (b) Test H0 : β2 = 0 versus H0 : β2 ≠ 0 with = .05. (c) Estimate the expe
> Referring to Example of the Data Bank, we now use two predictors, x1 = girth (cm) and x2 = length to predict y = weight (lb) of a polar bear. The output from a regression analysis. (a) How m any polar bears were included in the analysis? (b) Identify th
> Consider the data on all of the wolves in Table D.9 of the Data Bank concerning age (years) and canine length (mm). (a) Obtain the least squares fit of the straight line regression model Y = βo + β1x + e to predict canine length from age. (b) Obtain the
> Developers have built a small robotic vehicle that can travel over rough terrain. They recorded the time y, in minutes, that it takes to travel a fixed distance over various but similar terrains. For a fixed run, the robot's motor is set at a nominal spe
> Consider the linear regression model where β0 = -2, β1 = -1, and the normal random variable e has standard deviation 3. (a) What is the mean of the response Y when x = 3 ? When X = 5? (b) Will the response at x = 3 always be lar
> Graph the straight line for the means of a linear regression model Y = β0 + β1x + e having β0 = 7 and β1 = 2.
> Under the linear regression model: (a) Determine the mean and standard deviation of Y, for x = 1, when β0 = 3, β1 = -2, and ( = 3. (b) Repeat part(a) with x = 2.
> The weights (oz) of nineteen babies born in Madison, Wisconsin, are summarized in the computer output Locate two measures of center tendency, or location, and interpret the values.
> Under the linear regression model: (a) Determine the mean and standard deviation of Y, for x = 3, when βo = 1, β1 = 5, and ( = 4. (b) Repeat part(a) with x = 2.
> Show that the SS due to regression, S2xy / Sxx, can also be expressed as β^21 Sxx.
> (a) Show that the sample correlation coefficient rand the slope β^1 of the fitted regression line are related as (b) Show that SSE = (1 - r2) Syy·
> Refer to Exercise 11.30. According to the computer output in Table 8, find the proportion of y variability explained by x. Data from Exercise 11.30: According to the computer output in Table 8: (a) What model is fitted7 (b) Test, with a = .05, if the
> Identify the values of the parameters βo, β1, and (; in the statistical model Y = 6 - 3x + e where e is a normal random variable with mean O and standard deviation 3.
> Refer to Exercise 11.28. According to the computer output in Table 7, find the proportion of y variability explained by x. Also, calculate R2 from the analysis of variance table. Data from Exercise 11.28: According to the computer output in Table 7: (a
> Refer to Exercise 11.25. (a) What proportion of y variability is explained by the linear regression on x? (b) Find the sample correlation coefficient. Data from Exercise 11.25: An engineer found that by adding small amounts of a compound to rechargeabl
> Refer to Exercise 11.22. (a) What proportion of the y variability is explained by the linear regression on x? (b) Find the sample correlation coefficient. Data from Exercise 11.22: We all typically go to the shortest line in the grocery store. Data we
> Refer to Exercise 11.35 but consider the prediction of Internet penetration when the human development index is the predictor variable. (a) Determine the proportion of variation in Internet penetration that is explained by linear regression. (b) Compar
> Refer to Example 10 and Exercise 11.26, concerning the prediction of a human development index by Internet penetration, where; Det ermine the proportion of variation in y that is explained by linear regression. Data from Exercise 11.26: One measure of t
> In 2017, there were eight skyscrapers in the world over 500 meters tall. The ordered heights are 508 530 541 555 594 601 632 828 (a) Calculate the sample mean height for the eight skyscrapers. (b) Drop the largest value and recalculate the mean
> Refer to the summary statistics for polar bear and body length. (a) If you predict weight from girth, what percentage of the variation in weight will be explained by the least squares straight line based on girth? (b) If you predict girth from weight, w
> Based on a study of over 143,000 students, from 110 schools, investigators2 estimate the correlation between SAT scores and first year college grade point ratios by r = .35. If you predict first year college grades from the SAT score, what percentage of
> Consider the data on male wolves of the Data Bank concerning age (years) and canine length (mm). (a) Obtain the least squares fit of canine length to the predictor age. (b) Test H0 : β1 = 0versus H1 : β1 ≠ 0 with = .05. (c) Obtain a 90% confidence i
> According to the computer output in Table 8: (a) Predict the mean response when x = 3 . (b) Find a 90% confidence interval for the mean response when x = 3. You will need the additional information n = 25, x = 1.793, and L (x; - x)2 = 1.848. (c) Find a
> According to the computer output in Table 8: (a) What model is fitted7 (b) Test, with a = .05, if the x term is needed in the model.
> Identify the values of the parameters βo, β1, and (; in the statistical model Y = -3 + 4x + e where e is a normal random variable with mean O and standard deviation 2.
> According to the computer output in Table 7: (a) Predict the mean response when x = 5000. (b) Find a 90% confidence interval for the mean response when x = 5000. You will need the additional information n = 30, x = 8354, and Σ(x; - x)2 =
> According to the computer output in Table 7: (a) What model is fitted? (b) Test, with a = .05, if the x term is needed in the model.
> Refer to Exercise 11.26. (a) Obtain the least squares estimates by fitting a straight line to the response Internet penetration using the predictor variable HDI. (b) Test, with a = .05, H0 : β1 = 0 versus a two-sided alternative. (c) Obtai
> One measure of the development of a country is the Human Development Index (HD I). Life expectancy, literacy, educational attainment, and gross domestic product per capita are combined into an index between O and 1 , inclusive with 1 being the highest de
> With reference to the radiation leakage data given in Exercise 2.15: (a) Calculate the sample mean. (b) Which gives a better indication of the amount of radiation leakage, the sample mean or the median? Data from Exercise 2.15: Before microwave ovens
> An engineer found that by adding small amounts of a compound to rechargeable batteries during manufacture, she could extend their lifetimes. She experimented with different amounts of the additive (g) and measured the hours they lasted in a laptop. (a) C
> Refer to Exercise 11.22. Obtain a 95% confidence interval for . Interpret. Data from Exercise 11.22: We all typically go to the shortest line in the grocery store. Data were collected on the number of carts ahead in
> Refer to Exercise 11.22. Construct a 90% confidence interval for the intercept β0. Interpret. Data from Exercise 11.22: We all typically go to the shortest line in the grocery store. Data were collected on the number of carts ahead in line a
> We all typically go to the shortest line in the grocery store. Data were collected on the number of carts ahead in line and the total time to check out (minutes), including time in line, on five occasions. (a) Calculate the least squares estimates Î
> Referring to the formulas of β^0 and β^1, show that the point ( x, y ) lies on the fitted regression line.
> To see why the residuals always sum to zero, refer to the formulas of β^0 and β^1 and verify that (a) The predicted values are (b) The residuals are Then show that (c) Verify that = Syy – S2xy / Sxx
> Identify the predictor variable x and the response variable y in each of the following situations. (a) A training director wishes to study the relationship between the duration of training for new recruits and their performance in a skilled job. (b) The
> Using the formulas of β^1 and SSE, show that SSE can also be expressed as (a) SSE = Syy - β^1Sxy (b) SSE = Syy - β^21Sxx
> Refer to the data on female wolves in Exercise 11.17. (a) Obtain the least squares fit of body length to the predictor body weight. (b) Calculate the residual sum of squares. (c) Estimate (2. (d) Compare your answer in part (a) with your answer to part
> The data on female wolves in the Data Bank concerning body weight (lb) and body length (cm) are (a) Obtain the least squares fit of body weight to the predictor body length. (b) Calculate the residual sum of squares. (c) Estimate (2.
> A sample of six university students responded to the question, "How much time, in minutes, did you spend on the social network site yesterday?" One student never used the site and was dropped from the study. 100 45 60 130 30 Calculate the sample me
> A student hourly employee does small secret arial projects. The number of projects she completes in a day is the response variable y. The number of hours she works in a day is the predictor variable x. (a) Calculate x, y, Sxx, Sxy, and SYY. (b) Calculate
> A help desk devoted to student software problems also receives phone calls. The number of persons that can be served in person, within one hour, is the response y. The predictor variable, x, is the number of phone calls answered. (a) Calculate x, y , Sxx
> Refer to Exercise 11.12. (a) Find the residuals and verify that they sum to zero. (b) Calculate the residual sum of squares SSE by (i) Adding the squares of the residuals. (ii) Using the formula SSE = SYY – S2xy/Sxx. (c) Obtain the
> Refer to Exercise 11.11. (a) Find the residuals and verify that they sum to zero. (b) Calculate the residual sum of squares SSE by (i) Adding the squares of the residuals. (ii) Using the formula SSE = Syy – S2xy/Sxx. (c) Obtain the
> The office manager at a real estate firm makes a pot of coffee every morning. The time before it runs out, y, in hours depends on the number of persons working inside that day, x . Suppose that the pairs of ( x, y) values from six days are: (a) Plot the
> A student collected data on the number of large pizzas consumed, y, while x students are watching a professional football game on TV. Suppose that the data from five games are: (a) Construct a scatter diagram. (b) Calculate x, y, Sxx , Sxy , and SYY. (c)
> Consider the following linear regression model Y = β0 + β1x + e where β0 = 4, β1 = 3, and the normal random variable e has the standard deviation 4. (a) What is the mean of the response Y when x = 4? When x = 5? (b) Will the response at x = 5 always be
> Plot the line y = 2 + 3x by locating the points for x = I and x = 4. What is its intercept? What is its slope?
> Perform a test to determine if there is a significant difference between the population mean scores in Exercise 10.8. Use a = .OS. Data from Exercise 10.8: Rural and urban students are to be compared on the basis of their scores on a nationwide musical
> Rural and urban students are to be compared on the basis of their scores on a nationwide musical aptitude test. Two random samples of sizes 90 and 100 are selected from rural and urban seventh grade students. The summary statistics from the test scores
> Records show that in Las Vegas, NV, the normal daily maximum temperature (°F) for each month starting in January is 56 62 68 77 87 99 105 102 95 82 66 57 Verify that the mean of these figures is 79.67. Comment on the claim that the daily max
> One semester, an instructor taught the same computer course at two universities located in different cities. He was able to give the same final at both locations. The student's scores provided the summary statistics. (a) Obtain a point estimate of Â
> According to the assumptions underlying the two independent samples design, let the first population be N ( 5, 3 ) and the second be N ( 9, 6 ). Identify the values of the parameters µ1, (1, µ2, (2.
> A major clinical trial of a new vaccine for type-B hepatitis was conducted with a high-risk group of 1083 male volunteers. From this group, 549 men were given the vaccine and the other 534 a placebo. A follow-up of all these individuals yielded the data:
> According to the assumptions underlying the two independent samples design, (a) Are two observations from the same sample, say X2 and X4 , (i) Independent? (ii) Do they always have the same distribution? (b) Are two observations from different sample
> In the survey on which the Data Bank is based, a larger number of persons was asked to respond to the statement "I would characterize my political beliefs as liberal" on a seven point Likert scale from strongly disagree (1) to strongly agree (7). A count
