Question: Using a die, generate a sample and

> 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.

> 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

> 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

> Suppose the number of different computers used by a student last week 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

> If the double-stem display still has too few stems, we may wish to construct a stem-and-leaf display with a separate stem to hold leaves O and I, 2 and 3, 4 and 5, 6 and 7, and a stem to hold 8 and 9. The resulting stem-and-leaf display is called a five-

> Using the sampling distribution determined for X = ( X1 + X2 ) / 2, verify that E [X] = µ and

> Using the sampling distribution determined for X = ( X1 + X2 ) / 2, verify that E [X] = µ and

> Determine the standard deviation of X for a random sample of size (a) 9, (b) 36, and ( c) 144. ( d) How does quadrupling the sample size change the standard deviation of X?

> The data suggests that one plausible model, for X = the number of accidents in one month, is a population distribution having mean µ = 2.6 and variance (2 = 2.4. Determine the standard deviation of X for a random sample of size (a) 25, (b) 100, and ( c)

> Refer to the data on earthquakes of magnitude greater than 6.5. The data suggests that one plausible model, for X = magnitude, is a population distribution having mean µ = 7 .OS and standard deviation u = .43. Calculate the expected value and standard de

> Refer to the velocity data for females. One plausible model for the population distribution has mean µ = 31.2 and standard deviation c, = 8.62 feet per second. Calculate the mean and standard deviation of X for a random sample of size (a) 4 and (b) 25.

> The population density function and that for the sampling distribution of X, for n = 2, are shown in Figure 6. Identify which one is the sampling distribution and explain your answer.

> Th e population density function and that for the sampling 2 distribution of X are shown in Figure 5. Identify which one is the sampling distribution and explain your answer.

> Identify each of the following as either a parameter or a statistic. (a) Population standard deviation. (b) Sample interquartile range. (c) Population 20th percentile. (d) Sample first quartile. (e) Sample median.

> A file cabinet has 8 student folders arranged alphabetically according to last name. Three files are selected at random. (a) How many different selections are possible? (b) Find the probability that the selected folders are all adjacent.

> If there are too many leaves on some stems in a stem-and-leaf display, we might double the number of stems. The leaves 0- 4 could hang on one stem and 5- 9 on the repeated stem. For the observations. We would get the double-stem display Construct a doubl

> A box of tulip bulbs contains six bulbs that produce yellow flowers and five bulbs that produce red flowers. Four bulbs are to be randomly selected without replacement. Find the probability that: (a) Exactly two of the select ed bulbs produce red flower

> Refer to Exercise 4.91, and further suppose that the 5 respondents who are below 30 consist of 2 males and 3 females, whereas those above 30 consist of 4 males and 2 females. Now, the researcher wants to randomly select 2 males and 2 females to be assign

> An advertisement seeking volunteers for a clinical research draws 11 respondents. Of these respondents, 5 are below age 30 and 6 are over 30. The researcher will randomly select 4 persons to assign to a particular treatment regimen. (a) How many selecti

> Are the following methods of selection likely to produce a random sample of 5 students from your school? Explain. (a) Pick 5 students throwing flying discs on the mall. (b) Pick 5 students who are studying in the library on Friday night. (c) Select 5

> There are four elementary outcomes in a sample space. If P(e1) = .3, P(e2) = .4, and P(e3) = .2, what is the probability of e4?

> In one area city park, there are 15 trees, of which 9 are bushy and 6 that are not bushy. If 5 trees are selected at random to receive a new spray, what is the probability that exactly 3 bushy trees are selected?

> Nine agricultural plots for an experiment are laid out in a square grid as shown. Three plots are to be selected at random . (a) Find the probability that all 3 are in the same row. (b) Find the probability that all 3 are in different rows.

> A college senior is selected at random from each state. Next, one senior is selected at random from the group of 50. Does this procedure produce a senior selected at random from those in the United States?

> Refer to Exercise 4.85. Suppose the sampling of 3 alternators is done by randomly choosing one after another and without replacement. The event A can then be described as G 1 G2G3, where G denotes "good" and the suffixes refer to the order of the draws.

> A batch of 18 used automobile alternators contains 4 defectives. If 3 alternators are sampled at random, find the probability of the event (a) A = [ None of the defectives appear] (b) B = [ Exactly two defectives appear ]

> The following is a stem-and-leaf display with two-digit leaves. (The leading leaf digit = 10.0.) List the corresponding measurements.

> A local company is giving away five streaming devices to persons who visit its website and register on a specified day. Each person is allowed to register three times for the drawing. If, at the time of drawing, there are 6200 entries, what is the probab

> After a preliminary screening, the list of qualified jurors consists of 10 males and 7 females. The 5 jurors the judge selects from this list are all males. Did the selection process seem to discriminate against females? Answer this by computing the prob

> Out of 12 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired . (a) How many distinct p airs are possible? (b) In how many of the pairs will O or 1 person not be able to do the work? (c) If two persons are chos

> A psych ologist will select 5 preschool children from a class of 11 students in order to try out new abuse awareness material. (a) How many different selections are possible? (b) Suppose 4 of the 11 children are males. If the 5 selected children were t

> If a coin is tossed 11 times, the outcome can be recorded as an 11-character sequence of H's and T's according to the results of the successive tosses. In h ow m any ways can there be 4 H's and 7 T's? (Put differently, in how many ways can one choose 4 p

> Consider the following experiment: A coin will be tossed twice. If both tosses show heads, the experiment will stop. If one head is obtained in the two tosses, the coin will be tossed one more time, and in the case of both tails in the two tosses, the co