Question: Referring to Exercise 8.4, suppose that

> 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

> The number of PCBs (polychlorinated biphenyls) was measured in 40 samples of soil that were treated with contaminated sludge. The following summary statistics were obtained. x = 3.56, s = .5 ppm (a) Obtain a 95% confidence interval for the population mea

> Refer to the data on the girth, in centimeters, of grizzly b ears in Table D.6 of the Data Bank. A computer calculation gives (a) Does the 95% confidence interval cover the true mean girth of all grizzly bears in the area of the study? Explain. (b) Why

> To study the growth of pine trees at an early stage, a nursery worker records 40 measurements of the heights (cm) of one-year-old red pine seedlings. ( courtesy of Professor Alan Ek). The summary statistics are n = 40, x = 1.715, s = .475 centimeter Fi

> Refer to the data on the growth of female salmon in the marine environment in the Dat Bank. A computer calculation gives a 9 5% confidence interval. (a) Does the 95% confidence interval cover the true mean growth of all fem ale salmon in that marine envi

> Radiation measurements on a sample of 65 microwave ovens produced x = .11 and s = .06. Determine a 95% confidence interval for the mean radiation.

> Refer to the 40 height measurements given in Exercise 8.3, which have n = 40, x = 1.715, s = .475 centimeter Calculate a 99% confidence interval for the population mean height. Data from Exercise 8.3: To study the growth of pine trees at an early stag

> Refer to Exercise 5.8. Assuming each choice is equally likely, determine the prob ability distribution of X. Data from Exercise 5.8: A child psychologist interested in how friends are selected studies groups of three children. For one group, Ann, Barb,

> An employee of an on-campus copy center wants to determine the mean number of copies before a cartridge needs to be replaced. She records the life length in thousands of copies for 43 cartridges and obtains n = 43, x = 8.12, s = 1.78 thousand copies Obta

> Refer to the Statistics in the stiffness of lumber. A computer calculation gives x = 1.596 and s = .3872 for the n = 100 measurements of stiffness. Find a 95% confidence interval for the mean stiffness.

> In a study to determine whether a certain stimulant produces hyperactivity, 44 mice were injected with 10 micrograms of the stimulant. Afterward, each mouse was given a hyperactivity rating score. The mean score was x = 15.3 and s = 2.4. Give a 95% confi

> A credit company randomly selected 50 contested items and recorded the dollar amount being contested. These contested items h ad a sample mean x = 95.74 dollars and s = 24.63 dollars. Construct a 95% confidence interval for the mean amount contested, µ.

> 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

> Based on a survey of 140 employed persons in a city, the mean and standard deviation of the commuting distances between home and the principal place of business are found to be 8.6 and 4.3 miles, respectively. Determine a 90% confidence interval for the

> Referring to Example, where the 158 times to complete the firefighter test have mean 307. 77 and standard deviation 51.852, obtain a 99% confidence interval for the mean time of all possible recruits who would complete the test.

> A researcher asked participants to wear a simple counting device for a week and they counted the number of times that they thought about food. Determine a point estimate of the daily mean number of times a person thinks about food and the (1 - a)% error

> The freshness of produce at a superstore is rated on a scale of 1 to 5 with 5 being very fresh . From a random sample of 49 customers, the average score was 3.8 with a standard deviation of .7. (a) Obtain a 95% confidence interval for the population mean

> Students are asked about the number of songs they downloaded from a pay-for-songs Web site the last month. From a random sample of 39 students, the sample mean was 4. 7 with a standard deviation of 3.2. (a) Obtain a 95% confidence interval forµ, the mea

> Refer to Exercise 5.7. Suppose that for each purchase P(B) = ½ and the decisions in different weeks are independent. Assign probabilities to the elementary outcomes and obtain the distribution of X. Data from Exercise 5.7: Each week a grocery shopper bu

> In a study designed to find differences in personality between cat and dog lovers, 3 subjects were first classified according to their answers to a questionnaire about attitudes towards pets, and previous pet ownership. The n = 66 subjects classified as

> In a study on the nutritional qualities of fast foods, the amount of fat was measured for a random sample of 35 hamburgers of a p articular restaurant chain. The sample mean and standard deviation were found to be 30 .2 and 3.8 grams, respectively. Use t

> A nutritionist records the time to eat an evening meal, at a student cafeteria, for 64 students. She obtains x = 36.2 and s = 5.6 minutes and reports that the 95% confidence interval for the mean time to eat is or (30.79, 41.6 1) (a) Is this statement c

> Each day of the year, a large sample of cellular phone calls is selected and a 95% confidence interval is calculated for the mean length of all cellular phone calls on that day. Of these 365 confidence intervals, one for each day of the year, approximate

> A company wants to check the consistency of electronic copies of signatures for consumer credit purchases. A sample of 49 electronic signatures are available from the same customer. One measure of consistency in signing is the total length that the scrip

> Table records the number of items returned by 30 persons to a large discount department store in late December. The summary statistics are n = 30, x = 2.538, s = 1.303 Obtain a 98% confidence interval for µ, the population mean number of items returned

> To estimate µ with a 90% error margin of 2.9 units, one has determined that the required sample size is 108. What then is the required sample size if one wants the 95% error margin to be 1.8 units?

> A researcher wants to estimate µ, the mean number of minutes before a person scores over 200 on a new computer game. She wishes to get estimates, separately, for each of the groups (a) novices, (b) occasional game players, and ( c) expert game players. W

> Find the standardized variable Z if X has (a) Mean 13 and standard deviation 3. (b) Mean 57 and standard deviation 16. (c) Mean 142 and variance 36.

> The probability distribution of X is given by the function for x = 0, 1, 2, 3 Find (a) P [ X = 1 ] (b) P [ X is odd ].

> Which of the distributions in Figure 3 are compatible with the following statements? (a) The first test was too easy because over half the class scored above the mean. (b) In spite of recent large increases in salary, half of the professional football

> If a student is more likely to be late than on time for the 1:20 PM history class: (a) Determine if the median of the student's arrival time distribution is earlier than, equal to, or later than 1:20 PM. (b) On the basis of the given information, can yo

> Determine the 15th percentile of the curve in Exercise 6.1. Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?

> Refer to the volume of timber data. (a) Make a normal-scores plot of the original data. (b) Make a normal-scores plot of the fourth root of the data. (c) Compare the two plots and comment.

> The MINITAB computer language makes it possible to easily transform data. With the data already set in column 1 , the commands will place the natural logarithm loge x in C2, √x in C3, and X1/4 in C4. Normal-scores plots can then be cons

> Use MINITAB or another package program to make a normal-scores plot of the lizards' speed test. Comment on the pattern.

> Use MINITAB or another package program to make a normal-scores plot of the College Qualification Test (CQT) data. Comment on the pattern.

> Use MINITAB or another package program to make a normal-scores plot of the malt extract data in the Data Bank.

> Determine the median and the quartiles for the curve depicted in Exercise 6.1. Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?

> Use a computer program to make a normal-scores plot for the volume of timber data in Table 4. (Courtesy of Professor Alan Ek) Comment on the departure from normality displayed by the normal-scores plot. We illustrate a normal-scores plot using MINITAB. W

> For each case, list the values of X and f (x) and examine if the specification represents a probability distribution. If it does not, state what properties are violated. (a) f( x ) = 1/6 (x – 1) for x = 1, 2, 3, 4 (b) f( x ) = x – 2 for x = 0, 2, 4 (c) f

> Suppose that 20% of the trees in a forest are infested with a certain type of parasite. (a) What is the probability that, in a random sample of 300 trees, the number of trees having the parasite will be between 49 and 71 inclusive? (b) After sampling 3

> In a large midwestern university, 30% of the students live in apartments. If 200 students are randomly selected, find the probability that the number of them living in apartments will be between 55 and 70 inclusive.

> The weekly amount spent by a small company for in-state travel has approximately a normal distribution with mean $1450 and standard deviation $220. What is the probability that the actual expenses will exceed $1560 in 20 or more weeks during the next yea

> A survey reports that 96% of the people think that violence has increased in the past five years. Out of a random sample of 50 persons, 48 expressed the opinion that citizens have become more violent in the past five years. Does the normal approximation

> The unemployment rate in a city is 7.9%. A sample of 300 persons is selected from the labor force. Approximate the probability that (a) Less than 18 unemployed persons are in the sample. (b) More than 30 unemployed persons are in the sample.

> The median age of residents of the United States is 37.2 years. If a survey of 200 residents is taken, approximate the probability that at least 110 will be under 37.2 years of age.

> Copy Figure 16 and add the standard score scale Underneath the x-axis for n = 5, 12, 25. Notice how the distributions center on zero and most of the probability lies between z = -2 and z = 2.

> State whether or not the normal approximation to the binomial is appropriate in each of the following situations. (a) n = 90, p = .24 (b) n = 100, p = .03 (c) n= 120, p = .98 (d) n= 6 1, p = .40

> A recent study reported that 54% of the adults in the United States drink at least one cup of coffee a day. Suppose that this is still the current rate. What is the normal approximation to the probability that, in a random sample of 1000 adults, the numb

> Determine the median and the quartiles for the probability distribution depicted in Exercise 6.1(a). Data from Exercise 6.1: Which of the functions sketched below could be a probability density function for a continuous random variable? Why or why not?

> Examine if the following are legitimate probability distributions.

> A study by the National Endowment of the Arts revealed that 19.7% of adults age 18-24 played a musical instrument in the past 12 months. Suppose that is still the current rate. What is the normal approximation to the probability, that in a random sample

> Let the number of successes X have a binomial distribution with n = 20 and p = .5 (a) Find the exact probability of each of the following (b) Apply the normal approximation to each situation in part (a).

> Let the number of successes X have a binomial distribution with n = 25 and p = .6 (a) Find the exact probabilities of each of the following: (b) Apply the normal approximation to each situation in part (a).

> It is reasonable to model the distribution that produced the lizards' speed test as normal distribution with mean 1.7 mis and standard deviation .57 m is. Find the probability that the speed of a new lizard (a) Will exceed 2.5 m is. (b) Will be less th

> The time for an emergency medical squad to arrive at the sports center at the edge of town is distributed as a normal variable with µ = 17 minutes and ( = 3 minutes. (a) Determine the probability that the time to arrive is: (i) More than 22 minutes. (

> Suppose the contents of bottles of water coming off a production line have a normal distribution with mean 9.1 ounces and standard deviation .1 ounce. (a) If every bottle is labeled 9 ounces, what proportion of the bottles contain less than the labeled a

> Refer to Exercise 6. IO where, according to current U.S. Census Bureau data, the heights of 20- to 29-year-old women can be well approximated by a normal distribution with mean 64.1 inches and standard deviation 3.1 inches. (a) What is the probability t

> Th e diameter of hail hitting the ground during a storm is normally distributed with a mean of .5 inch and a standard deviation of .1 inch . What is the probability that: (a) A hailstone picked up at random will have a diameter greater than . 71 inch ?

> The weights of apples served at a restaurant are normally distributed with a mean of 5 ounces and standard deviation of 1.2 ounces. What is the probability that the next person served will be given an apple that weighs less than 4 ounces?

> Th e time it takes a symphony orchestra to play Beethoven's Ninth Symphony has a normal distribution with a mean of 64.3 minutes and a standard deviation of 1.15 minutes. The next time it is played, what is the probability that it will take between 62.5

> Let the random variable X represent the sum of the points in two tosses of a die. (a) List the possible values of X. (b) For each value of X, list the corresponding elementary outcomes. (c) Obtain the probability distribution of X .

> For the curve f(x) graphed in Exercise 6.1(c), which of the two intervals [ 0 < X < .5] or [ 1.5 < X < 2] is assigned a higher probability?

> According to the children's growth chart that doctors use as a reference, the heights of two-year old boys are nearly normally distributed with a mean of 34.5 inches and a standard deviation of 1.4 inches. If a two-year-old boy is selected at random, wha

> It is reasonable to model the distribution that produced the College Qualification Test (CQT) data as a normal distribution with mean 150 and standard deviation 25.4. (a) What is the probability of a new student scoring above 195? (b) What score has prob

> Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 500 and a standard deviation of 100. Find the probability that a student will score: (a) Over 650. (b) Less than 250. (c) Between 325 and 675.

> Referring to Exercise 6.25, find b such that (a) P[ X < b] = .7995 (b) P [ X > b ] = .002 (c) P[X < b ] = .015 Data from Exercise 6.25: Data suggests that the normal distribution with mean 13.0 and standard deviation 2.4 is a plausible model for the

> Data suggests that the normal distribution with mean 13.0 and standard deviation 2.4 is a plausible model for the length (feet) of adult anaconda snakes. Find (a) P[X < 10.4 ] (b) P [ X ≤ 17.8 ] (c) P [ X > 17.8 ] (d) P[X > 16. 72 ] (e) P [10.24 ≤ X ≤ 1

> Find (a) P(Z. < .14) (b) The 14th percentile of Z. (c) P(Z < .86) (d) The 86th percentile of Z.

> Find (a) P [Z < .33 ]. (b) The 33rd percentile of the standard normal distribution. (c) P [Z < .97 ]. (d) The 97th percentile of the standard normal distribution.

> Find the quartiles of the standard normal distribution.

> Find the z value in each of the following cases . (a) P[Z < z ] = .1762 (b) P[Z > z ] = .10 (c) P[-z < Z < z ] = .954 (d) P[-.6 < Z < z ] = .50

> Refer to Exercise 5.9 but let X denote the maximum years’ experience among the two persons selected. (a) List all choices and the corresponding values of X. (b) List the distinct values of X . (c) Obtain the probability distribution of X. Data from E

> Identify each of the following as a discrete or continuous random variable. (a) Number of empty seats on a flight from Atlanta to London. (b) Yearly low temperature in your city. (c) The height of the highest wave on the north shore of Hawaii next winter

> On flights from San Francisco to Chicago, the number of empty seats are to be grouped into the following classes: 0-4, 5- 9, 10- 14, 15- 19, more than 19. Is it possible to determine from this frequency distribution the exact number of flights on which t

> The weights of the players on the university football team (to the nearest pound) are to be grouped into the following classes: 160-175, 175-190, 190-205, 205-220, 220-235, 235 or more. The left endpoint is included but not the right endpoint. Explain wh

> Cities must find better ways to dispose of solid waste. According to the Environmental Protection Agency, in a recent year, the composition of solid municipal waste was (a) Determine the percentage of other materials in the solid waste. This category inc