Question: A student collected data on the number

> 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.

> Graph the straight line for the means of the linear regression model having β0 = 3, 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 &Icirc

> 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

> 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 &Acirc

> 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

> A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. By observing 150 smokers and 250 nonsmokers, the researcher finds that 95 of the smokers and 103 of the nonsmokers have prominent wrinkles around their eyes. (a)

> Refer to Exercise 10.46. Let the population proportions in the two groups who have ≤ 8 hours of sleep per night be denoted by p1 and p2. Construct a 95% confidence interval for p1 – p2· Data from Exerc

> Random samples of 250 persons in the 30- to 40-year age group and 250 persons in the 60- to 70-year age group are asked about the average number of hours they sleep per night, and the following summary data are recorded. Do these data demonstrate that th

> Referring to the data of Exercise 10.44, calculate a 95% confidence interval for the difference between the survival rates for the two groups. Data from Exercise 10.44: The popular disinfectant Listerine is named after Joseph Lister, a British physician

> The popular disinfectant Listerine is named after Joseph Lister, a British physician who pioneered the use of antiseptics. Lister conjectured that human infections might have an organic origin and thus could be prevented by using a disinfectant. Over a p

> The monthly income in dollars for seven sales persons at a car dealership are 2450 2275 2425 4700 2650 2350 2475 (a) Calculate the mean and median salary. (b) Which of the two is preferable as a measure of center and why?

> Refer to the measurement of job satisfaction. Using the data in Exercise 10.12, compare the proportion of very satisfied for firefighters, p1, with the proportion for office supervisors, p2. (a) Find a 95% confidence interval for the difference of propo

> Refer to the measurement of job satisfaction. Rather than average score, researchers often prefer the proportion who respond "very satisfied." Using the data in Exercise 10.12, compare the proportion for clergy, p1, with the proportion for office supervi

> A study about the effects of marijuana use concludes that persons who became persistent users before they reached the age of 18, and who remained persistent users until age 38, will lose several IQ points over that time span. The summary data, for the ch

> Laser guns for detecting speeders require an accurate measurement of distance. In one daily calibration test, police measure the known distances 164 and 104 feet. The difference in readings should be 60 but there is some variation. The differences ( cour

> Identify the following as either matched pair or independent samples. Also identify the experimental units, treatments, and response in each case. (a) Twelve persons are given a high-potency vitamin C capsule once a day. Another twelve do not take extra

> In an experiment conducted to see if electrical pricing policies can affect consumer behavior, 10 homeowners in Wisconsin had to pay a premium for power use during the peak hours. They were offered lower off-peak rates. For each home, the July on-peak us

> Two methods of memorizing difficult material are being tested to determine if one produces better retention. Nine pairs of students are included in the study. The students in each pair are matched according to IQ and academic background and then assigned

> A study is to be made of the relative effectiveness of two kinds of cough medicines in increasing sleep. Six people with colds are given medicine A the first night and medicine B the second night. Their hours of sleep each night are recorded. (a) Establi

> A manufacturer claims his boot waterproofing is better than the major brand. Five pairs of shoes are available for a test. (a) Explain how you would conduct a paired sample test. (b) Write down your assignment of waterproofing to each shoe. How did you

> It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following data are collect ed concerning the weekly loss of working hours due to accidents in six plants both before and afte

> With reference to the water quality in Exercise 2.17: (a) Find the sample mean. (b) Does the sample mean or the median give a better indication of the water quality of a "typical" day? Why? Data from Exercise 2.17: The city of Madison regularly checks

> Two sun blockers are to be compared. One blocker is rubbed on one side of a subject's back and the other blocker is rubbed on the other side. Each subject then lies in the sun for two hours. After waiting an additional hour, each side is rated according

> Given the following matched pairs sample, (a) Evaluate the t statistic (b) How many degrees of freedom does this t have?

> A scientist developing a dietary supplement for rabbits decides to give a new supplement to IO rabbits and but not to 10 other rabbits who will serve as a control. (a) Briefly explain why it is important to randomly divide the rabbits in two groups. Wha

> Observations on 10 mothers who nursed their babies and 8 who did not revealed that nursing mothers felt warmer toward their babies. Can we conclude that nursing affects a mother's feelings toward her child?

> Early studies showed a disproportionate number of heavy smokers among lung cancer patients. One scientist theorized that the presence of a particular gene could tend to make a person want to smoke and be susceptible to lung cancer. (a) H ow would random

> Six students in a psychology course have volunteered to serve as subjects in a match ed pairs experiment. (a) List all possible sets of p airings if subjects are paired by age. (b) If subjects are p aired by gender, how many p airs are available for the

> Randomly allocate three subjects from among 6 mice, Alpha, Tau, O mega, Pi, Beta, Phi to group I.

> Randomly allocate 2 subjects from among Al, Bob, Carol, Ellen, John to be in the control group. The others will receive a treatment.

> Using the approximate t distribution, obtain a 95% confidence interval for the difference of means.

> Refer to Exercise 10.24 (c). In addition, x = 21.1 and y = 15.4. Test H0 : µ1 - µ2 = 0versus H1 : µ1 - µ2 > 0 at level a = .05. Data from Exercise 10.24: Given here are the sample sizes and the sample standard deviations for independent random samples f

> The height that bread rises may be one indicator of how light it will be. As a first step, before modifying her existing recipe, a student cook measured the raise height (cm) on eight occasions: 6.3 6.9 5.7 5.4 5.6 5.5 6.6 6.5 Find the mean and me

> Twenty college students were asked for their number of close friends; persons who showed sympathy when needed and helped in hard times. Th e average number reported was just over 2. Identify a statistical population and the sample.

> Given the samples 4 6 5 and 9 6 3 (a) Evaluate the d.f. for testing H0 : µ1 = µ2 = 0 using the approximate t statistic. (b) Use software to confirm your d.f. in part (a).

> Given here are the sample sizes and the sample standard deviations for independent random samples from two populations. For each case, state which of the three tests you would use in testing hypotheses about µ1 - µ2 : (1) Z test, (2) t test with pooling,

> In the experiment, the logarithm of the percent transfer was also measured on twenty different tiles at 30 seconds. Using the summary statistics for both cases apply the two-sample t test for the one-sided alternative that the transfer is larger at 30 se

> Does the shape of the glass influence h ow fast a person drinks? As part of a larger study, some participants drank lager from a 12-ounce glass that was either curved or had straight sides. To distract them, they were told their task was to find words in

> To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random and trained by method 1; the remaining 10 workers are trained by method 2. After completion of

> The data on the weight (lb) of male and female wolves, from the Data Bank, are (a) Test the null hypothesis that the mean weights of males and females are equal versus a two-sided alternative. Take a = .05. (b) Obtain a 95% confidence interval for the

> Six mice - Alpha, Tau, Omega, Pi, Beta, and Phi- are to serve as subjects. List all possible ways to split them into two groups with the first having 4 mice and the second 2 mice.

> Two gel pens, G el-1 and Gel-2, are compared on the basis of the number of weeks before they stop writing. Out of 27 persons available, 13 are randomly chosen to receive Gel-1 and the other 14 receive Gel-2. These are the only pens they use for writing.

> Three male and three female students recorded the number of times they used a credit card in one week. (a) Calculate s2pooled. (b) Give an estimate of the common standard deviation for the number of uses. (c) Evaluate the t statistic for testing equalit

> Suppose that measurements of the size of butterfly wings (cm) for two related species yielded the data (a) Calculate s2pooled. (b) Give an estimate of the common standard deviation for the wing size for the two species. (c) Evaluate the t statistic for

> Calculate the mean and median for each of the following data sets. (a) 3 6 2 5 4 (b) 4 3 8 5 (c) -4 0 -3 -1 2 -1 0

> The generic output below summarizes the data, given in Data Bank, on the pretest percent body fat in male and female students. Find a 99% confidence interval for the difference of mean percent body fat.