Question: The following measurements of the diameters (in

> Concern over the quality of eyeglasses purchased over the internet led to a study where many glasses were individually ordered from several different online vendors. Among the lenses with only antireflective coating, 61 had a thickness at the center grea

> Sugar content (g) and carbohydrate content (g) are obtained from the package of the breakfast cereals. (a) Calculate the sample mean carbohydrates for all 30 cereals. (b) Construct a table using carbohydrates rather than sugar. (c) Calculate the relati

> Applicants for welfare are allowed an appeals process when they feel they have been unfairly treated. At the hearing, the applicant may choose self-representation or representation by an attorney. The appeal may result in an increase, decrease, or no cha

> A company that manufactures car mufflers finds that the labor to set up and run a nearly automatic machine has mean µ = 1.9 hours and ( = 1.2 hours. For a random sample of 36 runs. (a) Determine the mean and standard deviation of X¯. (b) What can you sa

> A random sample of size 150 is taken from the population of the ages of juniors enrolled at a large university during one semester. This population has mean 21.1 years and standard deviation 2.6. The population distribution is not normal. (a) Is it reas

> With reference to Exercise 2.48, calculate the quartiles. Data from Exercise 2.48: A large mail-order firm employs numerous persons to take phone orders. Computers on which orders are entered also automatically collect data on phone activity. One variab

> Suppose that the size of pebbles in a river bed is normally distributed with mean 12.1 mm and standard deviation 3.2 mm. A random sample of 9 pebbles are measured. Let X¯ denote the average size of the sampled pebbles. (a) What is the distribution of X¯

> The weights of pears in an orchard are normally distributed with mean .32 pound and standard deviation .08 pound . (a) If one pear is selected at random, what is the probability that its weight is between .28 and .34 pound7 (b) If X denotes the average

> 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. For a random sample of size n = 9 . (a) What are the mean and standard deviation of X¯? (b) What is the distribut

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

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

> What sample size is required in order that the standard deviation of X be: (a) 1/4 of the population standard deviation? (b) 1/7 of the population standard deviation? (c) 12 % of the population standard deviation?

> Refer to Exercise 7.34 and, instead of X, consider the statistic Sample range R Largest observation - Smallest observation For instance, if the sample observations are (2, 6), the range is 6 - 2 = 4. (a) Calculate the sample range for all possible sampl

> As a very extreme case of self-selection, imagine a five-foot-high solid wood fence surrounding a collection of Great Danes and Miniature Poodles. You want to estimate the proportion of Great Danes inside and decide to collect your sample by observing th

> The United States Environmental Protection Agency reports that in 2014, each American generated 4.44 pounds of solid waste. (a) Does this mean every single American produces the same amount of garbage? What do you think this statement means? (b) Was th

> Eight young students need mentors. Of these, there are three whom you enjoy being with while you are indifferent about the others. Two of the students will be randomly assigned to you. Label the students you like by 0, 1, and 2 and the others by 3, 4, 5,

> A large mail-order firm employs numerous persons to take phone orders. Computers on which orders are entered also automatically collect data on phone activity. One variable useful for planning staffing levels is the number of calls per shift handled by e

> Fifty band members would like to ride the b and bus to an out-of-town game. However, there is room for only 44. Use Table I, Appendix B, to select the 44 persons who will go. Determine how to make your selection by taking only a few two-digit selections.

> There are 9 sites on a large campus at which bicycles are parked as part of a shared bicycle program in the city. Use Table I, to select 3 sites to visit and record the number of bicycles available at noon during a weekday.

> Two-person sailboats are available for use at the university dock. Your group is large enough to need three of them . Use Table 1, to select your three boats from among the 10 that are in a line along the shore.

> What is wrong with this statement of purpose? PURPOSE: Determine if it takes too long to get cash from the automated teller machine during the lunch hour. Give an improved statement of purpose.

> Which of the following are anecdotal and which are based on a sample? (a) Tom says he gets the best prices on electronics at the www.best elc.com Internet site. (b) Out of 22 students, 6 had multiple credit cards. (c) Among 55 people checking in at th

> Which of the following are anecdotal and which are based on sample? (a) Out of 200 students questioned, 40 admitted they lied regularly. (b) Bobbie says the produce at Market W is the freshest in the city. (c) Out of 50 persons interviewed at a shoppi

> Each year a local weekly newspaper gives out "Best of the City" awards in categories such as restaurant, deli, pastry shop, and so on. Readers are asked to fill in their favorites on a form at the web site of the weekly paper. The establishment receiving

> A magazine that features the latest electronics and computer software for homes enclosed a short questionnaire on a postcard. Readers were asked to answer questions concerning their use and ownership of various software and hardware products, and to then

> It is often easy to put off doing an unpleasant task. At a Website, persons can take a test and receive a score that determines if they have a serious problem with procrastination. Should the scores from people who take this test online be considered a r

> An interested student used the method of least squares to fit the straight line y^ = 850. 7 + 320.3x to gross domestic product, y, in real dollars. The results for 26 recent years, x = 1, 2, ... , 26, appear here. Which assumption for a linear regression

> Refer to the data of college qualification test scores given in Exercise 2.22. (a) Find the median. (b) Find Q1 and Q3. Data from Exercise 2.22: The following data represent the scores of 40 students on a college qualification test (courtesy of R. W.

> A student is asked to estimate the mean height of all male students on campus. She decides to use the heights of members of the basketball team because they are conveniently printed in the game program. (a) Identify the statistical population and the sa

> Consider the population of persons living in Chicago. You want to learn about the proportion of eligible voters who are registered to vote. (a) Specify the population unit. (b) Specify the variable of interest. (c) Specify the statistical population.

> Consider the population of all students at your college. You want to learn about total monthly entertainment expenses for a student. (a) Specify the population unit. (b) Specify the variable of interest. (c) Specify the statistical population.

> A newspaper headline reads, College Students Display An Inability To Tell Fake News from Real and the article explains this conclusion was reached from the responses of 2300 students at ten colleges concerning whether or not a case of social media type n

> Refer to the green gas made by two catalysts. Perform a Wilcoxon rank sum test with the intention of showing that catalyst l produces larger product volume. Take a approximately equal to .05.

> The possible synergetic effect of insecticides and herbicides is a matter of concern to many environmentalists. It is feared that farmers who apply both herbicides and insecticides to a crop may enhance the toxicity of the insecticide beyond the desired

> A project (courtesy of Howard Garber) is constructed to prevent the decline of intellectual performance in children who have a high risk of the most common type of mental retardation, called cultural-familial. It is believed that this can be accomplished

> Referring to the data in Exercise 15.5, is there strong evidence of a difference in the serum phosphate level between the two breeds? Data from Example 15.5: The following data pertain to the serum calcium measurements in units of IU/L and the serum alk

> The following data pertain to the serum calcium measurements in units of IU/L and the serum alkaline phosphate measurements in units of µg/ml for two breeds of pigs, Chester White and Hampshire: Using the Wilcoxon rank-sum procedure, test if

> The number of breathing pauses per hour (BPH) helps determine a sleeping disorder. We took a random sample of 3 males, population A, and a random sample of 2 females and obtained the values of BPH (a) Evaluate WA. (b) Evaluate WS.

> With reference to Exercise 2.3, calculate the quartiles. Data from Exercise 2.3: A student at the University of Wisconsin surveyed 40 students in her dorm concerning their participation in extracurricular activities during the past week. The data on num

> Using Appendix B, Table 8, find: (a) P[WS ≥ 44] when nA = 5, nB = 7. (b) P[WS ≤ 19] when nA = 6, nB = 5. (c) The point c such that P [WS ≥ c] is close to .05 when nA = 8, nB = 8.

> Determine the significance probability of rSP = .4, using the one-sided test, when n = 40.

> The following scores are obtained on a test of dexterity and aggression administered to a random sample of 10 high school seniors. Evaluate Spearman's statistic.

> The data for the contaminated lake are Evaluate rSP and verify your answer using software.

> Refer to Exercise 11.26 and the first four countries in Table 7. Internet penetration and the human development index (HDI) are Calculate Spearman's rank correlation. Data from Exercise 11.26: Using Appendix B, Table 8, find: (a) P [ Ws â‰&ye

> Charles Darwin performed an experiment to determine if self-fertilized and cross-fertilized plants have different growth rates. Pairs of Zea mays plants, one self- and the other cross-fertilized, were planted in pots, and their heights were measured afte

> Independent samples of sizes nA = 2 and nB = 5 are taken from two continuous populations. (a) Enumerate all possible collections of ranks associated with population A. Also attach probabilities to these rank collections assuming that the populations are

> We presented data on the blood pressure of 15 persons before and after they took a pill. (a) Perform a sign test, with a near .05, to determine if blood pressure has decreased after taking the pill. (b) Perform a Wilcoxon signed-rank test to det ermine

> A married couple's monthly credit charges are divided into his and hers and the difference, husband's minus wife's, is calculated. A random sample of 30 married couples yielded the Wilcoxon signed-rank statistic T+ = 325. What is the significance probabi

> The null distribution of the Wilcoxon signed-rank statistic T+ is det ermined from the fact that under the null hypothesis of a symmetric distribution about zero, each of the ranks 1, 2, ... , n is equally likely to be associated with a positive sign or

> Referring to Exercise 15.13, apply the Wilcoxon signed-rank test with a near .05. Data from Exercise 15.13: Two critics rate the service at six award-winning restaurants on a continuous 0 to 10 scale. Is there a difference between the critics' ratings?

> Use Appendix B, Table 9, to find: (a) P ( T+ ≥ 65 ] when n = 12. (b) P ( T+ ≤ 10] when n = 10. (c) The value c such that P [ T+ ≥ c ] = .039 when n = 8. (d) The values c1 and c2 such that P ( T+ &

> A social researcher interviews 25 newly married couples. Each husband and wife are independently asked the question: "How m any children would you like to have?" The following data are obtained. Do the data show a significant difference of opinion betwee

> Two critics rate the service at six award-winning restaurants on a continuous 0 to 10 scale. Is there a difference between the critics' ratings? (a) Use the sign test with a below .05. (b) Find the significance probability.

> In a taste test of two chocolate chip cookie recipes, 13 out of 17 subjects favored recipe A. Using the sign test, find the significance probability when H1 states that recipe A is preferable.

> One aspect of a study of gender differences involves the play behavior of monkeys during the first year of life ( courtesy of H. Harlow, U. W. Primate Laboratory). Six male and six female monkeys are observed in groups of four families during several ten

> If nA = 1 and nB = 14, find (a) The rank configuration that most strongly supports H1 : Population A is shifted to the right of population B. (b) The null probability of WA = 15. (c) Is it possible to have a = .05 with these sample sizes?

> Independent random samples of sizes nA = 4 and nB = 2 are taken from two continuous populations. (a) Enumerate all possible collections of ranks associated with the smaller sample in the combined sample ranking. Attach probabilities to these rank collect

> Using Appendix B, Table 7 , find the upper 10% point of the F for (a) d.f. = (4, 5) (b) d.f. = (4, 10) (c) d.f. = (4, 15) (d) d.f. = (4, 30) (e) Use software to verify your answers. (f) What effect does increasing the denominator d.f. have on the percen

> Using Appendix B, Table 7 for percentage points for the F distribution, find (a) The upper 5% point when v1 = 5 and v2 = 12. (b) The upper 5% point when v1 = 12 and v2 = 5. ( c) Use software to verify your answers to Part a and Part b.

> If you were to use the data on the length of major league baseball games in Exercise 2.43 to estimate the total amount of digital memory needed to film another 10 major league baseball games, which is the more meaningful description, the sample mean or t

> Reading levels vary between different magazines. To avoid difficulties caused by different typefaces and sizes, an investigator just count ed the number of letters and punctuation signs. Random samples of 20 sentences were selected from The New Yorker, S

> The abilities of six different brand athletic socks to wick moisture are rated. The rating is based on the time to reach l % moisture content after being subjected to a gentle mist. Use the relations for sums of squares and d.f. to complete the following

> An investigator wonders how the frequency of checking a smart phone varies with current activity. Students are assigned to one of four conditions: listening to a lecture, studying, eating a meal, or on a date. The response they record is the number of ti

> Refer to Exercise 14.28. Present the ANOVA table. What conclusions can you draw from th e two F tests? Take  = .05 . Data from Exercise 14.28: The yield, in pounds, of three types of heritage tomatoes (treatments) is obtained after pl

> Since restaurant C had unacceptable scores, it was decided to concentrate on the other restaurants. Five additional students are assigned to these restaurants. Suppose the quality scores, for all 11 visits combined, are Repeat Exercise 14.2 using these d

> Three loaves of bread, each made according to a different recipe, are baked in one oven at the same time. Because of possible uncontrolled variations in oven performance, each baking is treated as a block. This procedure is repeat ed five times, and the

> The yield, in pounds, of three types of heritage tomatoes (treatments) is obtained after planting them in three equal sized plots within a site (block). Types are randomly assigned to plots. A total of four different sites are used. Suppose the data are

> Refer to Exercise 14.25. Present the ANOVA table. What conclusions can you draw from the two F tests? Take  = .05. Data from Exercise 14.25: The hours of relief are measured under a placebo, Brand A, and Brand B sinus medicines. Call

> Suppose you wish to compare three different brands of tick collars for dogs. You have available three of each of the breeds Poodle, Lab, Collie, and Dachshund. Explain h ow you would assign a brand of tick collar to each of the 12 dogs in order to conduc

> On opening day one season, 10 major league baseball games were played and they lasted the following numbers of minutes. 167 211 187 176 170 158 198 218 145 232 Find the sample median.

> The hours of relief are measured under a placebo, Brand A, and Brand B sinus medicines. Call these treatment 1, treatment 2, and treatment 3, respectively. They are each given in succession, in random order, to each subject with two days between each tre

> Refer to the MINITAB commands but also check the box Store residuals. Graph the residuals from an ANOVA of the iris data. (a) In a normal-scores plot using all of the residuals. (b) Individual normal-scores plots for each type of iris.

> Referring to the density of bread data in Exercise 14.14, plot the residuals (a) In a dot plot using all of the residuals. (b) Individual dot plots for each recipe. Data from Exercise 14.14: Three bread recipes are to be compared with respect to densit

> Referring to the sound distortion data in Example 1, graph the residuals in (a) A dot plot using all of the residuals. (b) Individual dot plots for each model of earbuds.

> Determine the expression for the length of the t interval for µ1 - µ2 and the multiple-t interval for µ1 - µ2 when m = 10. The ratio of lengths does not depend on the data. Evaluate this ratio for a = .10 and n - k = 15.

> A study was conducted to examine the degree that the length of gestation influences school achievement for children born in the normal range of 3 7 to 41 weeks gestation. Academic achievement was measured by a third grade reading test that we summarize f

> Subjects must press a button when they h ear a signal. The three treatments are three different intensities of the signal. The time elapsed between presentation of the signal and when the button is pushed, are recorded in hundredths of a second. Suppose

> As suggested by the photo in the beginning of this chapter, consumers can rate new HDTVs. Many Web sites use a five point scale. Although the individual responses are not normal, the central limit result applied to each of the four samples does justify t

> Construct the 90% multiple-t confidence intervals using the sound distortion data in Example 1.

> Taking a = .OS and n - k = 26, determine the appropriate percentile of the t distribution when calculating the multiple-t confidence intervals with (a) m = 3 and (b)m = 5.

> Physical education researchers interested in the development of the overarm throw measured the horizontal velocity of a thrown ball at the time of release. The results for first-grade children (in feet/second) (courtesy of L. Halverson and M. Roberton) a

> Refer to the data on reading levels in Exercise 14.7. Test for equality of means. Take a = .05. Data from Exercise 14.7: Reading levels vary between different magazines. To avoid difficulties caused by different typefaces and sizes, an investigator just

> Test for equality of means based on the travel expense data in Exercise 14.6. Take  = .05. Data from Exercise 14.6: Referring to the lying experiment. The subjects were also able to cheat on the tax form by claiming excessive travel e

> Three bread recipes are to be compared with respect to density of the loaf. Five loaves will be baked using each recipe. (a) If one loaf is made and baked at a time, how would you select the order? (b) Given the following data, conduct an F test for equa

> Test for equality of means based on the data in Exercise 14.2. Take  = .05. Data from Exercise 14.2: Subjects must press a button when they h ear a signal. The three treatments are three different intensities of the signal. The time e

> 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