Assume that the standard deviation of the number of violent incidents in one hour of children's shows on television is 3.2. An investigator would like to be 99% sure that the true mean number of violent incidents per hour is estimated within 1.4 incidents. For how many randomly selected hours does she need to count the number of violent incidents?
> The weights from a random sample of 20 golden retriever dogs have mean 76.1 pounds and standard deviation 5.9 pounds. Assume that the weights of the dogs have a normal distribution. (a) Construct a 98% confidence interval for the population mean. (b) Wh
> Use software to find the probability (a) T ≤ -1 .3 when d.f = 12. (b) T > 1.7 when d.f = 21. (c) |T| > 1.35 when d.f = 33. (d) Find c such that P [T > c] = .015 when d.f = 18. (e) Find c such that P [I T l > c] = .04 when d.f = 42.
> Record the t.05 values for d.f of 5, 10, 15, 20, and 29. Does this percentile increase or decrease with increasing degrees of freedom?
> Use software to find the number b so that (a) P[T < b] = .95 when d.f = 5. (b) P[ - b < T < b] = .95 when d.f = 37. (c) P[T > b] = .01 when d.f 2. (d) P[ T > b] = .99 when d.f = 13.
> Do the data in Exercise 9.22 substantiate the conjecture that the true standard deviation of the acidity measurements is larger than 0.4? Test at a = .05. Data from Exercise 9.22: Measurements of the acidity (pH) of rain samples were recorded at 13 site
> Referring to Exercise 9.21, construct a 95% confidence interval for the population standard deviation of the diameters of Indian mounds. Data from Exercise 9.21: The following measurements of the diameters (in feet) of Indian mounds in southern Wisconsi
> Refer to the data of lizard lengths in Exercise 9.10. (a) Determine a 90% confidence interval for the population standard deviation (. (b) Should H0 : ( = 9 be rejected in favor of H1 : ( ≠9 at a = .10? Data from Exercise 9.10: A zo
> Based on recent records, the manager of a car painting center has determined the following probability distribution for the number of customers per day. (a) If the center has the capacity to serve two customers per day, what is the probability that one o
> During manufacture, the thickness of laser printer paper is monitored. Data from several random samples each day during the year suggest that thickness follows a normal distribution. A sample of n = 10 thickness measurements (ten-thousandths inch) yields
> Refer to Exercise 9.41. Construct a 95% confidence interval for the true standard deviation of the thickness of sheets produced on this shift. Data from Exercise 9.41: Plastic sheets produced by a machine are periodically monitored for possible fluctuat
> Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. Uncontrollable heterogeneity in the viscosity of the liquid mold makes some variation in thickness measurements unavoidable. However, if the true stan
> Find a 90% confidence interval for (, based on the n = 40 measurements of heights of red pine seedlings. State any assumption you make about the population.
> Use software to find (a) T < -1.729 when d.f = 19. (b) |T| > 2.179 when d.f = 12. (c) -1.703 < T < 1. 703 when d.f 27. (d) -1.833 < T < 2.821 when d.f. 9.
> Use software to find the probability (a) x2 ≤ 17.2 when d .f = 9. (b) x2 > 13.7 when d.f. = 23. (c) Find c such that P(x2 > c) = .015 when d.f = 12. ( d) Find c such that P ( x2 < c) = .04 when d.f. = 33.
> Using MINITAB software to compute x2 percentiles. (a) Determine x2.05 for the x2 distribution with d.f = 19. (b) Determine P (x2 ≤ 30) for d.f. = 19. Repeat Part (a) but click on Cumulative probability. (c) Do both parts with d.f. = 11
> Name the x2 percentiles shown and find their values. (c) Find the percentile in part (a) if d.f = 37. (d) Find the percentile in part (b) if d.f = 11. (e) Verify your answers above using software.
> Using the t able for the x2 distributions, find: (a) The upper 5% point when d.f = 8. (b) The upper 1% point when d.f = 16. (c) The lower 2.5% point when d.f. = 9. (d) The lower 1% point when d.f = 27. (e) Verify your answers above using software.
> Establish the connection between the large sample Z test, which rejects H0 : µ = µ0 in favor of H1 : µ ≠µ0 , at a = .05, if and the 95% confidence interval
> Among six new apps available this month, only three will prove to be useful to you in the long run. Suppose you purchase three of the apps at random. Find the probability distribution of X, the number of useful apps you select.
> Refer to the data in Exercise 9.33. (a) Construct a 90% confidence interval forµ. (b) If you were to test H0 : µ = 17 versus H1 : µ ≠ 17 at a = . 10, what would you conclude from your result in part (a}? Why? (c) Perform the hypothesis test indicated
> Ten participants tried a new weight loss diet for two months. The resulting weight losses (pounds} are 20.2 11.0 15.4 9.9 7.9 15.6 15.5 23.1 11.0 11.4 (a) Construct a 95% confidence interval for the population mean amount µ of decrease in weight
> The petal width (mm} of one kind of iris has a normal distribution. Suppose that, from a random sample of widths, the t based 90% confidence interval for the population mean width is ( 16.8, 19.6 } mm. Answer each question "yes," "no," or "can't tell," a
> The 90% confidence interval for the mean weight of female wolves was found to be ( 67.13, 80.62} pounds. (a} What is the conclusion of testing H0 : µ = 81 versus H 1 : µ ≠ 81 at level a = .10? (b} What is the conclusion if H0 : µ = 69?
> Based on a random sample of tail lengths for 15 male kites, an investigator calculates the 95% confidence interval (183.0, 195.0} mm based on the t distribution. The normal assumption is reasonable. (a} What is the conclusion of the t test for H0 : µ = 1
> Using MINITAB software to compute t percentiles (a) Determine t.05 for the t-distribution with d.f = 27. Cale > Probability Distributions > t.... Click on inverse.... Type 27 in Degrees of Freedom. Click Input constant and Type .95. Click OK. (b) Determ
> Refer to the computer anxiety scores for female accounting students in Data Bank. A computer calculation for a test of H0 : µ = 2 versus H1 : µ ≠2 is given here. (a) What is the conclusion if you test with a =
> A few years ago, noon bicycle traffic past a busy section of campus had a mean of µ = 300. To see if any change in traffic has occurred, counts were taken for a sample of 15 weekdays. It was found that x = 340 and s = 30. (a) Construct an a = .05 test o
> The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the company that produces this paint contemplates that adding a new chemical ingredient to the paint will accelerate the drying process. To investigate thi
> The ability of a grocery store scanner to read accurately is measured in terms of maximum attenuation (db). In one test with 20 different products, the values of this measurement had a mean 10.7 and standard deviation 2.4. The normal assumption is reason
> Use the approximate probability distribution to calculate (a) P(X ≤ 3] (b) P(X ≥ 2] (c) P(2 ≤ X ≤ 3]
> The data on the weight (lb) of female wolves, Test the null hypothesis that the mean weight of females is 83 pounds versus a two-sided alternative. Take a = .05.
> Refer to the experiment described in Example 3. In another 20 trials, a piece of watermelon was dropped on inoculated tiles. The summary statistics for the logarithm of percent transfer, measured at 5 seconds, are n = 20, x = 1.52, s = .09 (a) Find a 95%
> Refer to Exercise 9.10, where a zoologist collected 20 wild lizards in the southwestern United States. Do these data substantiate a claim that the mean length is greater than 128 mm? Test with a = .05. Data from Exercise 9.10: A zoologist collected 20 w
> Measurements of the acidity (pH) of rain samples were recorded at 13 sites in an industrial region. Determine a 95% confidence interval for the mean acidity of rain in that region.
> The following measurements of the diameters (in feet) of Indian mounds in southern Wisconsin were gathered by examining reports in Wisconsin Archeologist ( courtesy of J. Williams). (a) Do these data substantiate the conjecture that the population mean d
> Refer to the data on the weight (pounds) of male wolves given in the Data Bank. A computer calculation gives a 95% confidence interval. (a) Is the population mean weight for all male wolves in the Yukon-Charley Rivers National Reserve contained in this i
> Name the t percentiles shown and find their values from Appendix B, Table 5.
> The data on the lengths of anacondas on the front piece of the chapter yield a 95% confidence interval for the population mean length of all anaconda snakes in the area of the study. (a) Is the population mean length of all female anacondas living in th
> Refer to Exercise 9.12. Do these data support the claim that the mean monthly rent for a two-bedroom apartment differs from 1200 dollars7 Take  = .05. Data from Exercise 9.12: The monthly rent (dollars) for a two-bedroom apartment on
> Given the sample 4 7 5 4 (a) Evaluate the t-statistic for testing H0 : µ0 = 3. (b) Use software to check your value of t. R: t.test(x,mu=3) after x= c( 4, 7, 5, 4)
> In a study of the life length of a species of mice, 120 newborn mice are observed. The numbers staying alive past the first, second, third, and fourth years are 106, 72, 25, and 0, respectively. Let X denote the life length (in discrete units of whole ye
> One of the first investigations of the amount of persistent organic pollutants present in soil within an urban setting was motivated by a major flood seventy days earlier. 1 One series of measurements of the total amount of PCB congeners consisted of 14
> Henry Cavendish (1 731 - 1810) provided direct experimental evidence of Newton's law of universal gravitation, which specifies the force of attraction between two masses. In an experiment with known masses determined by weighing, the measured force can a
> From a random sample of size 18, a researcher states that (11.1, 15. 7) inches is a 90% confidence interval for µ, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval, obtain: (a) A point
> From a random sample of size 12, one has calculated the 95% confidence interval for µ and obtained the result (38.6, 46.2). (a) What are the x and s for that sample? (b) Calculate a 98% confidence interval for µ.
> The monthly rent (dollars) for a two-bedroom apartment on the west side of town was recorded for a sample of ten apartments. 1249 1590 1650 1625 1345 1725 1620 1200 1020 1200 Obtain a 95% confidence interval for the mean monthly rent for two-bed
> Eighteen samples of seaweed, each weighing 50 kilograms, are collected to study the feasibility of extracting protein for use in animal feed. The 18 determinations of protein yield have sample mean 3 .6 kilograms and standard deviation .8 kilogram. Dete
> A zoologist collected 20 wild lizards in the southwestern United States. The total length (mm) of each was measured. Obtain a 95% confidence interval for the mean length.
> Using the table for the t distributions, find: (a) The upper .05 point when d.f. = 6. (b) The lower .025 point when d.f = 10. (c) The lower .01 point when d.f 9. (d) The upper .10 point when d.f. = 13.
> When estimating the mean of a population, how large a sample is required in order that the 95% error margin be: (a) 1/8 of the population standard deviation? (b) 15% of the population standard deviation?
> Describe a procedure, based on 12 identical cards, that generates an observation from the probability distribution Specify appropriate numbers, one for each card, that make this probability distribution prevail for the number appearing on a randomly draw
> Refer to the box with the smiling face scale for rating cereals. Using the data that 30 out of 42 youngsters in a sample rated a cereal in the highest category, find an approximate 95% confidence interval for the corresponding population proportion.
> From telephone interviews with 1032 adults, it was found that 68% of those persons supported tougher legislation for antipollution measures. Does this poll substantiate the conjecture that more than 65% of the adult population are in favor of tough er le
> The same owners operate two coffee shops in a large building. One is (a) small and the other (b) large. On any day, the number of customers is only observed for one shop. Determine the point estimate ofµ, the mean number of persons served during a weekda
> An independent bank concerned about its customer base decided to conduct a survey of bank customers. Out of 505 customers who returned the survey form, 258 rated the overall bank services as excellent. (a) Test, at level a = .10, the null hypothesis tha
> Refer to Example where n = 5000 and proportion .78 of the students sometimes use cell phones while driving. Conduce a test of hypotheses, of size .05, with the intent of establishing that the population proportion is greater than . 75.
> Refer to Exercise 8.56. Perform a test of hypotheses to determine whether the proportion of ERS calls involving flat tires or lockouts was significantly smaller than .19, the true proportion for previous years. Data from Exercise 8.56: An automobile clu
> A concerned group of citizens wants to show that less than half the voters support the President's handling of a recent crisis. Let p = proportion of voters who support the handling of the crisis. (a) Determine H0 and H1. (b) If a random sample of 500
> An educator wishes to test H0 : p = .3 against H1 : p > .3, where p = proportion of college football players who graduate in four years. (a) State the test statistic and the rejection region for a large sample test having a = .05. (b) If 22 out of a ran
> A manager of a campus store that sells posters conjectures that more than 30% of all freshman dorm rooms have a poster of a rock group. From n = 60 rooms selected at random, an investigator records X = number of rooms having a poster of a rock group. (a
> Given here are the observed sample proportions p^ in the contexts of parts (a-d.) of Exercise 8.62. Calculate the test statistic and draw a conclusion of the test at the specified level of significance. (a) p^ = .233 (b) p^ = .72 ( c) p^ = .54 (d) Cl
> A probability distribution is partially given in the following table with the additional information that the even values of X are equally likely. Determine the missing entries in the table.
> Identify the variable as a discrete or a continuous random variable in parts (a)- ( e). (a) The loss of weight following a diet program. (b) The magnitude of an earthquake as measured on the open-ended Richter scale. (c) The seating capacity of a roller
> Each part of this problem specifies a claim about a population proportion, the sample size n, and the desired level of significance a. Formulate (i) the hypotheses, (ii) the test statistic, and (iii) the rejection region. (a) Claim p (i) Ho : p = .32, H1
> Given here are the descriptive statements of some claims that one intends to establish on the basis of data. In each case, identify the null and the alternative hypotheses in terms of a population proportion p. (a) Of smokers who eventually quit smoking
> Identify the null and the alternative hypotheses in the following situations. (a) A university official believes that the proportion of students who currently hold part-time jobs has increased from the value .26 that prevailed four years ago. (b) A cab
> When estimating µ from a large sample, suppose that one has found the 95% error margin of X to be 10.4. From this information, determine: (a) The estimated S.E. of X. (b) The 90% error margin.
> Refer to Example 16 and the babies born to parents that both smoke. (a) Find a 90% confidence interval for the proportion of male babies born to parents that both smoke. (b) Does p lie in your interval obtained in part (a)? (c) Why are you 95% confiden
> Out of a sample of 94 purchases at the drive-up window of a fast-food establishment, 27 were made with a major credit card. (a) Estimate the proportion of sales made with a credit card. (b) Obtain the estimated standard error. (c) Find a 98% confidenc
> California Condors, birds with up to a nine foot wingspan, almost became extinct over 20 years ago. Then a program began where birds are raised in captivity and later released into the wild. According to the U.S. Fish and Wildlife Service, 157 out of 166
> An automobile club that pays for emergency road services (ERS) requested by its members wishes to estimate the proportions of the different types of ERS requests. Upon examining a sample of 2927 ERS calls, it finds that 1499 calls related to starting pro
> A national safety council wishes to estimate the proportion of automobile accidents that involve pedestrians. How large a sample of accident records must be examined to be 96% certain that the estimate does not differ from the true proportion by more tha
> In a psychological experiment, individuals are permitted to react to a stimulus in one of two ways, say, A or B. The experimenter wishes to estimate the proportion p of persons exhibiting reaction A. How m any persons should be included in the experiment
> A surprise quiz contains three multiple-choice questions: Question 1 has four suggested answers, Question 2 has three, and Question 3 has two. A completely unprepared student decides to choose the answers at random. Let X denote the number of questions t
> Software programs using artificial intelligence are now writing many stories. These so called robots have replaced humans as the authors of routine reports in sports, finance, and other areas. During the first seven days of September, the football pages
> Suppose that n units are randomly sampled and x number of the sampled units are found to have the characteristic of interest. In each case, (i) define p in the context of the problem, (ii) provide a point estimate of p and (iii) determine the 95% error m
> Refer to Exercise 8.50. Along with the determinations of BOD, the discharge of suspended solids (SS) was also monitored at the same site. The mean and standard deviation of the 43 determinations of SS were found to be 5710 and 1720 pounds per day, respec
> Biological oxygen demand (BOD) is an index of pollution that is monitored in the treated effluent of paper mills on a regular basis. From 43 determinations of BOD (in pounds per day) at a particular paper mill during the spring and summer months, the mea
> The weekly flier from a large box store always features many items having a mail-in rebate. A random sample of 50 submissions produced the summary statistics x = 43 and s = 7. 7 days for the time interval between submission and receipt of the rebate chec
> A company wishing to improve its customer service collected hold times from 75 randomly selected incoming calls to its hot line that were put on hold. These calls h ad sample mean hold time x = 3.4 minutes and s = 2.4 minutes. Is the claim that µ > 3.0 m
> In a given situation, suppose H0 was not rejected at a = .02. Answer the following questions as "yes," "no," or "can't tell" as the case may be. (a) Would H0 also be retained at a = .01? (b) Would H0 also be retained at a = .05? (c) Is the P-value sma
> A company wants to establish that the mean life of its batteries, when used in a wireless mouse, is over 183 days. The data consist of the life lengths of batteries in 64 different wireless mice. (a) Formulate the null and alternative hypotheses. (b) Wha
> Refer to Example 6 where, one day, the visits of n = 48 students to the social network site produced the summary statistics x = 35.96 minutes and s = 29. 11 minutes, n = 48 (a) Conduct a test of hypotheses with the intent of establishing that mean connec
> The weekly flier from a large box store always features many items having a mail-in rebate. A random sample of 50 submissions produced the summary statistics x = 43 and s = 7.7 days for the time interval between submission and receipt of the rebate check
> New video games are rated, by editors, at various Web sites ( e.g., www.gamespot.com). You are equally interested in five games that received editors' ratings of 10 10 10 9 9 on a ten point scale. Suppose you decide to randomly choose two games to pu
> Refer to the data on the girth, in centimeters, of grizzly bears in the Data Bank. A computer calculation for a test of H0 : µ = 100 centimeters versus H1 : µ ≠100 gives (a) What is the conclusion if you test
> Refer to the data on the growth of female salmon in the marine environment in the Data Bank. A computer calculation for a test of H0 : µ = 411 versus H1 : µ ≠411 is given below. (a) What is the conclusion if y
> An investigator at a large midwestern university wants to determine the typical weekly amount of time students work on part-time jobs. More particularly, he wants to test the null hypothesis that the mean time is 15 hours versus a two-sided alternative.
> With reference to Exercise 8.40, (a) test with a = .02. (b) Based on your decision in part (a), what error could you have possibly made? Explain in the context of the problem. Data from Exercise 8.40: With reference to Exercise 8.12, perform a test wi
> With reference to Exercise 8.12, perform a test with the intent of establishing that the mean number of items returned is greater than 2.0. Take a = .02. Data from Exercise 8.12: Table records the number of items returned by 30 persons to a large discou
> A credit company randomly selected 50 contested items and recorded the dollar amount being contested. These contested items had sample mean x = 95 .74 dollars and s = 24.63 dollars. Construct a point estimate for the population mean contested amount, µ,
> A market researcher wants to perform a test with the intent of establishing that his company's medium pump bottle of soap has a mean life greater than 40 days. Th e sample size is 70 and he knows (= 5.6. (a) If you set the rejection region to be R: X ≥
> Suppose that the observed values of the sample mean in the contexts of parts (a-d) of Exercise 8.37 are given as follows. Calculate the test statistic Z and state the conclusion with the specified . (a) x = 30.54 (b) x = 19.7 (c) x = 63.9 (d) x = -.45
> Each part (a-d) of this problem gives the population standard deviation (, the statement of a claim about µ, the sample size n, and the desired level of significance a. Formulate (i) the hypotheses, (ii) the test statistic Z, and (iii) the r
> For each situation (a- d) in Exercise 8.33, state which of the following three forms of the rejection region is appropriate when ( is known. Data from Exercise 8.33: Stated here are some claims or research hypotheses that are to be substantiated by samp
> Market researchers are concerned if people who view a commercial remember the product. They often make phone surveys two hours after a commercial is shown. Suppose that 20% of the people who watch one commercial remember the product two hours later. Four
> From an analysis of the sample data, suppose that the decision has been made to retain the null hypothesis. In the context of each part (a- d) of Exercise 8.33, answer the following questions. (a) In what circumstance is it a correct decision? (b) When
> From an analysis of the sample data, suppose that the decision has been to reject the null hypothesis. In the context of each part (a- d) of Exercise 8.33, answer the following questions: (a) In what circumstance is it a correct decision? (b) When is i
> Stated here are some claims or research hypotheses that are to be substantiated by sample data. In each case, identify the null hypothesis Ha and the alternative hypothesis H1 in terms of the population meanµ. (a) The mean time a health insurance compan
> A national fast food chain, with thousands of franchise locations, needed to audit the books at each location. They first selected a sample of 50 locations and performed the audit. They determined that a 9 5% confidence interval for the mean time to comp
