Question: A scientist developing a dietary supplement for

> 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

> 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 &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?

> 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.

> In the experiment, cat lovers were also scored on the Introversion/Extroversion scale. Using the summary statistics for both cases Dog lovers: n1 = 66, x = 6.12, s1 = 1.75 Cat lovers: n2 = 352, x = 4.81, s2 = 1.47 (a) Test the null hypothesis of equal me

> In a study of interspousal aggression and its possible effect on child behavior, the behavior problem checklist (BPC) scores were recorded for 47 children whose parents were classified as aggressive. The sample mean and standard deviation were 7.92 and 3

> Refer to the confidence interval obtained in Exercise 10.12(b). If you were to test the null hypothesis that the mean satisfaction scores are equal versus the two-sided alternatives, what would be the conclusion of your test with a = .057 Data from Exer

> Workers in three occupations were questioned about satisfaction with their jobs. Suppose the number of responses in each of the four categories are Assign l to very dissatisfied, 2 to a little dissatisfied, 3 to moderately satisfied, and 4 to very satisf

> Perform a test of hypothesis that is intended to show that the mean for magazine 1 is more than 2 words larger than the mean for magazine 2. (a) Formulate the null and alternative hypotheses. (b) State the test statistic and the rejection region with a =

> A linguist wants to compare the writing styles in two magazines and one measure is the number of words per sentence. On the basis of 50 randomly selected sentences from each source, she finds Determine a 98% confidence interval for the difference in mean

> Grades for first semester are compared to those for second semester. The five one-semester courses biology, chemistry, English , history, and psychology must be taken next year. (a) Make a list of all possible ways to split the courses into two groups w

> Referring to Exercise 7.8, use a die to generate samples of size 3. Investigate the sampling distribution of the number of times a value 1 occurs in a sample of size 3. (a) Roll the die and assign X = 1 if 1 dot shows and X = 0, otherwise. Repeat until

> Using a die, generate a sample and evaluate the statistic. Then repeat many times and obtain an estimate of the sampling distribution. In particular, investigate the sampling distribution of the median for a sample of size 3 from the population distribut

> Calculate the mean and median for each of the following data sets. (a) 2 10 3 6 4 (b) 3 2 7 4

> To determine the time a cashier spends on a customer in the express lane, the manager decides to record the time to check-out for the customer who is being served at 10 past the h our, 20 past the hour, and so on. Will measurements collected in this mann

> A bride-to-be asks a prospective wedding photographer to show a sample of her work. She provides ten pictures. Should the bride-to-be consider this a random sample of the quality of pictures she will get? Comment.

> A random sample of size 2 is selected, with replacement, from the set of numbers { 0, 2, 6 }. (a) List all possible samples and evaluate x and s2 for each . (b) Determine the sampling distribution of X. (c) Determine the sampling distribution of s2.

> From the set of numbers { 3, 5, 7 }, a random sample of size 2 is selected with replacement. (a) List all possible samples and evaluate x for each. (b) Determine the sampling distribution of X.

> Suppose 2 boards are needed for an application and the minimum stiffness of the two is of interest. (a) By row, take the SO minimums of the stiffness values for adj a cent pairs. Calculate their sample mean and standard deviation. Compare their sample m

> Suppose 2 boards are needed for an application and the average stiffness of the two is of interest. (a) By row, take the SO means of the stiffness values for adjacent pairs in Table 7. Calculate their sample mean and standard deviation. Compare their sam

> Data obtained from asking the wrong questions at the wrong time or in the wrong place can lead to misleading summary statistics. Explain why the following collection procedures are likely to produce useless data. (a) To evaluate the number of students w

> The number of complaints per day, X, received by a cable TV distributor has the probability distribution (a) Find the expected number of complaints per day. (b) Find the standard deviation of the number of complaints. (c) What is the probability distri

> Refer to Table 5 on page 223. (a) Calculate the sample median for each sample. (b) Construct a frequency table and make a histogram. (c) Compare the histogram for the median with that given in Figure 3 for the sample mean. Does your comparison suggest

> The weight of an almond is normally distributed with mean .05 ounce and standard deviation .01 5 ounce. Find the probability that a package of 100 almonds weighs between 4.8 and 5 .3 ounces. That is, find the probability that X is between .048 and .053 o

> Referring to Exercise 2.20, construct a five-stem display for the magnitude of earthquakes. Data from Exercise 2.20: In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.

> According to the growth chart that doctors use as a reference, the heights of two-year-old boys are normally distributed with mean 34.5 inches and standard deviation 1.3 inches. For a random sample of 6 two-year-old boys, find the probability that the sa

> The heights of male students at a university have a nearly normal distribution with mean 70 inches and standard deviation 2.8 inches. If 5 male students are randomly selected to make up an intramural basketball team, what is the probability that the heig

> The result of a recent survey suggests that one plausible population distribution, for X = number of persons with whom an adult discusses important matters, can be modeled as a population having mean µ = 2.0 and standard deviation a = 2.0. A random sampl

> The distribution of personal income of full-time retail clerks working in a large eastern city has µ = $51 ,000 and ( = $5000. (a) What is the approximate distribution for X based on a random sample of 100 persons? (b) Evaluate P ( X > 51 ,500].

> Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.4 ounces and standard deviation .4 ounce. (a) If every can is labeled 32 ounces, what proportion of the cans have contents that weigh less than the labeled

> A population has distribution Let X 1 and X2 be independent and each have the same distribution as the population. (a) Det ermine the missing elements in the table for the sampling distribution of X = (X1 + X2)/2. (b) Find the expected value of XÂ&

> According to a normal distribution with mean 115 and standard deviation 22 hundredths of an inch describes the variation in female salmon growth in freshwater. For a sample of size 6, determine the (a) Mean of X¯. (b) Standard deviation of X¯. (c) Dis

> Identify the parameter, statistic, and population when they appear in each of the following statements. (a) During a recent year, forty-one different movies received the distinction of generating the most box office revenue for a weekend. (b) A survey

> As suggested in Example 8, Chapter 6, the population of hours of sleep can be modeled as a normal distribution with mean 7. 2 hours and standard deviation 1.3 hours. For a sample of size 9, determine the (a) Mean of X¯. (b) Standard deviation of X¯. (c