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Statistics Principles And Methods 7th Edition Richard A. Johnson, Gouri K. Bhattacharyya - Solutions

Approximately 40% of the Wisconsin population have type O blood. If 4 persons are selected at random to be donors, find P[at least one type O].
The primary cooling unit in a nuclear power plant has reliability .999. There is also a back-up cooling unit to substitute for the primary unit when it fails. The reliability of the back-up unit is .910. Find the reliability of the cooling system of the power plant. Assume independence.
An accountant screens large batches of bills according to the following sampling inspection plan. She inspects 4 bills chosen at random from each batch and passes the batch if, among the 4, none is irregular. Find the probability that a batch will be passed if, in fact: (a) 5% of its bills are
In 80% of the cases an electronic scanner is successful in detecting flaws in a material specimen. Three material specimens containing flaws will be tested with the scanner. Assume that the tests are independent. (a) List the sample space and assign probabilities to the simple events. (b) Find the
Refer to Exercise 4.52. Given that a landfill selected at random is found to have a high concentration of mercury, what is the probability that its concentration is:(a) High in barium?(b) Low in both arsenic and barium?(c) High in either arsenic or barium?
Of the patients reporting to a clinic with the symptoms of sore throat and fever, 25% have strep throat, 40% have an allergy, and 10% have both. (a) What is the probability that a patient selected at random has strep throat, an allergy, or both? (b) Are the events "strep throat" and "allergy"
Consider tossing two fair coins and the events A: Head in the first toss B: Head in the second toss C: Both heads or both tails in the two tosses (a) Verify that the property of independence holds for all event pairs. (b) Show that P(ABC) is different from the product P(A) P(B) P(C). (This
Repeat Example 20 but change
Carol and Karl both solve difficult computer problems that come to the student desk. Carol makes 60% of the repairs and Karl 40%. However, Carol's repairs are incomplete 4% of the time and Karl's are incomplete 6% of the time.(a) Determine the probability that a repair is incomplete.(b) If a repair
In a county, men constitute 60% of the labor force. The rates of unemployment are 5.1% and 4.3% among males and females, respectively. (a) In the context, of selecting a worker at random from the country labor force, state what probabilities the foregoing percentages represent. (Use symbols such as
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 coin will be tossed two more times. (a) Make a
Refer to Example 21 concerning spam but now suppose that a new list is available. Among the 1000 messages, the 350 spam messages have 310 that contain words on this list and the 650 normal messages have 70 that contain words on the list.(a) Obtain the probability that a message is spam given that
In professional tennis, the server often tries to ace her opponent on the first serve. If the first serve is out of bounds, the server tries to be more accurate with the second and last serve. From records of women's tennis at Wimbledon3 the probability is .61 that the first serve is in bounds.
A large firm has 85% of its service calls made by a contractor, and 10 of these calls result in customer complaints. The other 15% of the service calls are made by their own employees, and these calls have a 5% complaint rate. Find the(a) Probability of receiving a complaint.(b) Probability that
Refer to Example 22 where a manufacturer had difficulty getting enough LED screens. Now suppose, because of the shortage, the manufacturer had to obtain 30% of the screens from the second supplier and 15% from the third supplier. Find the (a) Probability that a LED screen will be defective. (b)
Evaluate: (a) (6/3) (b) 10/4 (c) (22/2) (d) (22/20) (e) (30/3) (f) (30/27)
Of 10 available candidates for membership in a university committee, 6 are men and 4 are women. The committee is to consist of 4 persons. (a) How many different selections of the committee are possible? (b) How many selections are possible if the committee must have 2 men and 2 women?
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 differently, in how many ways can one choose 4 positions out of 11 to put the letter H?)
A psychologist 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 to consist of 2 males and 3 females, how many
Out of 12 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired. (a) How many distinct pairs are possible? (b) In how many of the pairs will 0 or 1 person not be able to do the work? (c) If two persons are chosen in a random manner, what is the probability
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 probability of having no female members in the
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?
Suppose you participate in a lottery conducted by a local store to give away four prizes. Each customer is allowed to place 2 cards in the barrel. Suppose the barrel contains 5000 cards from which the 4 winning cards will be chosen at random. What is the probability that at least one of your cards
A batch of 20 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]
Refer to Exercise 4.91. 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 G1G2G3, where G denotes "good" and the suffixes refer to the order of the draws. Use the method of Example 14 to calculate how
An instructor will choose 3 problems from a set of 7 containing 3 hard and 4 easy problems. If the selection is made at random, what is the probability that only the hard problems are chosen?
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.
In one area of an orchard, there are 17 trees, of which 10 are bushy and 7 lean. If 4 trees are randomly selected for testing a new spray, what is the probability that exactly 2 bushy trees are selected?
Referring to Exercise 4.96, now suppose that the trees are located in two rows: Row A has 8 trees of which 4 are bushy, and row B has 9 trees of which 6 are bushy. Two trees are to be randomly selected from each row for testing the spray, and the selections are independent for the two rows. (a)
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 selections are possible? (b) What is the probability
Water collected in a single bottle from a river is divided into eight specimens. Two specimens are randomly selected and sent to Lab A, two to Lab B, two to Lab C, and two to Lab D. The amount of heavy metals (ppm) is measured for each specimen. Calling each lab a treatment, suppose the data
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 turned on, subjects visually study a picture. The
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 test for equality of means taking a = .05.
Using the data from Exercise 14.1, test for equality of means using a = .05. Treatment Observations A............... 5 9 B............... 8 4 C............... 4 2 D............... 7 9
Test for equality of means based on the data in Exercise 14.2. Take a = .05.In Exercise 14.2
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 equality of means. Take a = .05.
Test for equality of means based on the travel expense data in Exercise 14.6. Take a = .05.In Exercise 14.6
Refer to the data on reading levels in Exercise 14.7. Test for equality of means. Take a = .05In Exercise 14.7
Taking a = .05 and n - k = 26, determine the appropriate percentile of the t distribution when calculating the multiple-r confidence intervals with (a) m = 3 and (b) m = 5.
Construct the 90% multiple-f confidence intervals using the sound distortion data in Example 1.
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 treating the treatment means as if the normal
Subjects must press a button when they hear 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 the data are(a) Obtain the arrays that show a
A study was conducted to examine the degree that the length of gestation influences school achievement for children born in the normal range of 37 to 41 weeks gestation. Academic achievement was measured by a third grade reading test that we summarize for the gestation periods 37, 39, and 41
Determine the expression for the length of the t interval for μ1 - μ2 and the multiple-r 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
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 ear buds.
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.In Exercise 14.14
Refer to the MINITAB commands in Exercise 14.37 but also check the box Store residuals. Next, referring to Exercise 6.55, graph the residuals from an ANOVA of the iris data in Exercise 14.38 (a) In a normal-scores plot using all of the residuals. (b) Individual normal-scores plots for each type of
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 treatment. Suppose the data are(a) Provide a
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 how you would assign a brand of tick collar to each of the 12 dogs in order to conduct a randomized block experiment.
Refer to Exercise 14.25. Present the ANOVA table. What conclusions can you draw from the two F tests? Take a = .05.
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(a) Provide a decomposition for the
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 repeated five times, and the following measurements of density are
It was decided to vary the experiment in Exercise 14.1 by dropping Lab D. Water from a single collection bottle was divided into eleven specimens. The amount of heavy metals (ppm) is measured for each specimen. Suppose the data are as follows and repeat Exercise 14.1.
Refer to Exercise 14.28. Present the ANOVA table. What conclusions can you draw from the two F tests? Take a = .05.In Exercise 14.28.
As part of a cooperative study on the nutritional quality of oats, 6 varieties of oat kernels with their hulls removed are subjected to a mineral analysis. The plants are grown according to a randomized block design, and the measurements of protein by percent of dry weight are recorded in Table
Referring to Exercise 14.31, suppose that variety 6 is of special interest. Construct simultaneous 90% confidence intervals for the differences between the mean of variety 6 and each of the other means.
Food scientists investigated whether making a cheese sauce by a continuous process or batch process made any difference to taste. They also included a third treatment, a carefully selected ideal product, that served as a control. Treatment 1 is the ideal, treatment 2 is the continuous process, and
Compute the sums of squares and construct the ANOVA table for the data given in Exercise14.33.In Exercise 14.33.
Refer to the data on travel expenses in Exercise 14.6 and the F-test in Exercise 14.15. It is the ordering of the population means, and the sizes of their differences, that is the key finding of study.(a) Calculate 95% simultaneous confidence intervals for the differences in means.(b) Are these
As part of the multi lab study, four fabrics are tested for flammability at the National Bureau of Standards. The following burn times in seconds are recorded after a paper tab is ignited on the hem of a dress made of each fabric.(a) State the statistical model and present the ANOVA table. With a =
Using the computer. MINITAB can be used for ANOVA. Start with the data on each treatment, from Example 1, set in separate columns. The sequence of commands and output is:Use computer software to analyze the moisture data in table 8
The iris data described in Example 6 are given in the stem-and-leaf diagrams below.The MINITAB output for the analysis of the iris data is given below. Individual 95% CIs For Mean Based on Pooled StDev (a) Identify the SSE and its degrees of freedom. Also locate s. (b) Check the calculation of F
Three different chemicals are compared on their ability to make fabric stain-resistent. Four bolts of cloth, manufactured weeks apart, are used. Because the results are expected to vary from bolt of cloth to bolt, three small samples are cut from each bolt and a different chemical is applied to
The abilities of six different brand athletic socks to wick moisture are rated. The rating is based on the time to reach 1% moisture content after being subjected to a gentle mist. Use the relations for sums of squares and d.f. to complete the following ANOVA table:
Refer to the output here concerning the time (min) it took four different persons (blocks) to complete three different tasks.(a) Identify the SSE and its degrees of freedom.(b) Are the block means different? Check the calculation of F for blocks from the given sums of squares and degrees of
Spots cannot always be removed by dry cleaning. Suppose the records from four different dry cleaning establishments yield the following data on number of un removable spots per day.Provide a decomposition of the observations and obtain the ANOVA table.
Referring to the lying experiment in Chapter 13. Example 6, the subjects were also able to cheat on the tax form by claiming excessive travel expenses for participating in the experiment. The subjects were randomly assigned to the three groups so the average amounts claimed should be similar unless
Using Appendix B, Table 7, find the upper 10% point of F for (a) d.f. = (3, 5) (b) d.f. = (3, 10) (c) d.f. = (3, 15) (d) d.f. = (3, 30) (e) What effect does increasing the denominator d.f. have?
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. (d) Time it takes for a plumber to fix a
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.
In the finals of a match play golf tournament, the winner will get $90,000 and the loser $15,000. Find the expected winnings of player B if (a) The two finalists are evenly matched and (b) Player B has probability .8 of winning.
The number of overnight emergency calls X to the answering service of a heating and air conditioning firm have the probabilities .05, .1, .15, .35, .20, and .15 for 0, 1, 2, 3, 4, and 5 calls, respectively.(a) Find the probability of fewer than 3 calls.(b) Determine E (X) and sd (X).
Suppose the number of parking tickets X issued during a police officer's shift has the probability distribution(a) Find the mean and standard deviation of the number of parking tickets issued.(b) Let A = [X 1 ]. Find P{A | B) = P(X 1).(c) Suppose the numbers of tickets issued on different days
A botany student is asked to match the popular names of three house plants with their obscure botanical names. Suppose the student never heard of these names and is trying to match by sheer guess. Let X denote the number of correct matches.(a) Obtain the probability distribution of X.(b) What is
The number of days, X, that it takes the post office to deliver a letter between City A and City B has the probability distributionx f(x)3...........................54.......................... .35.......................... .2Find:(a) The expected number of days.(b) The standard deviation of the
A roulette wheel has 38 slots, of which 18 are red, 18 black, and 2 green. A gambler will play three times, each time betting $5 on red. The gambler gets $10 if red occurs and loses the bet otherwise. Let X denote the net gain of the gambler in 3 plays (for instance, if he loses all three times,
Suppose that X can take the values 0, 1, 2, 3, and 4, and the probability distribution of X is incompletely specified by the functionFind (a) f(4) (b) P[X > 2] (c) E(X) and (d) sd(X).
A probability distribution can also be described by a function that gives the accumulated probability at or below each value of X. Specifically,Cumulative distribution function at c = Sum of probabilities of all values x For the probability distribution given here, we calculateF(l) = P[X F(2) = P[X
Let the random variable Y denote the proportion of times a head occurs in three tosses of a coin, that is, V = (No. of heads in 3 tosses)/3.(a) Obtain the probability distribution V.(b) Draw the probability histogram.(c) Calculate the E(Y) and sd(Y).
Is the model of Bernoulli trials plausible in each of the following situations? Identify any serious violations of the conditions. (a) A beginning golfer tries 40 putts, 5 feet from the hole, while practicing on the putting green. (b) Persons applying for a driver's license will be recorded as
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.
Give an example (different from those appearing in Exercise 5.109) of repeated trials with two possible outcomes where: (a) The model of Bernoulli trials is reasonable. (b) The condition of independence is violated. (c) The condition of equal P( S) is violated.
If the probability of having a male child is .5, find the probability that the third child is the first son.
A basketball team scores 35% of the times it gets the ball. Find the probability that the first basket occurs on its third possession. (Assume independence.)
The proportion of people having the blood type O in a large southern city is .4. For two randomly selected donors: (a) Find the probability of at least one type O. (b) Find the expected number of type O. (c) Repeat parts (a) and (b) if there are three donors.
A viral infection is spread by contact with an infected person. Let the probability that a healthy person gets the infection in one contact be p = .4. (a) An infected person has contact with six healthy persons. Specify the distribution of X = No. of persons who contract the infection. (b) Find P[X
The probability that a voter will believe a rumor about a politician is .3. If 20 voters are told individually: (a) Find the probability that none of the 20 believes the rumor. (b) Find the probability that seven or more believe the rumor. (c) Determine the mean and standard deviation of the number
National safety statistics suggest that about 33% of the persons treated in an emergency room because of moped accidents are under 16 years of age. Suppose you count the number of persons under 16 among the next 14 moped accident victims to come to the emergency room. (a) Find the mean of X. (b)
For each situation, state if a binomial distribution is reasonable for the random variable X. Justify your answer. (a) A multiple-choice examination consists of 10 problems, each of which has 5 suggested answers. A student marks answers by pure guesses (i.e., one answer is chosen at random out of
A school newspaper claims that 70% of the students support its view on a campus issue. A random sample of 20 students is taken, and 10 students agree with the newspaper. Find P[10 or less agree] if 70% support the view and comment on the plausibility of the claim.
Examine if the following are legitimate probability distributions.
At one large midwest university, about 40% of the college seniors have a social science major. Fourteen seniors are selected at random. Let X denote the number that have a social science major. Determine (a) P[3 < X < 9] (b) P[3 < X < 9] (c) P[3 < X < 9 ] (d) E(X) (e) sd(X)
Refer to the population of social science majors in Exercise 5.120 but change the sample size to n = 5. Using the binomial table, (a) List the probability distribution. (b) Plot the probability histogram. (c) Calculate E(X) and Var(X) from the entries in the list from part (a). (d) Calculate E(X) =
For a binomial distribution with p = .15, find the smallest number n such that 1 success is more probable than no successes in n trials.
Only 30% of the people in a large city feel that its mass transit system is adequate. If 20 persons are selected at random, find the probability that 10 or more will feel that the system is adequate. Find the probability that exactly 10 will feel that the system is adequate.
A sociologist feels that only half of the high school seniors capable of graduating from college go to college. Of 17 high school seniors who have the ability to graduate from college, find the probability that 12 or more will go to college if the sociologist is correct. Assume that the seniors
Jones claims to have extrasensory perception (ESP). In order to test the claim, a psychologist shows Jones five cards that carry different pictures. Then Jones is blindfolded and the psychologist selects one card and asks Jones to identify the picture. This process is repeated 16 times. Suppose, in
A manufacturer of luxury cars is experiencing some difficulties with a new metallic paint. During the final check at the end of assembly line, let X = be the number of painting imperfections per car. This random variable is described by a Poisson distribution mean 2.6. Determine the probability
A Poisson distribution describes X = the number of bad checks a mega-store receives each day. If this store receives an average of 2 bad checks per day, (a) Find the mean and variance. What are the probabilities it will receive (b) 3 bad checks in a given day? (c) 5 bad checks over any 2
Among the library's books purchased in the past three years, 1.2 % cannot be located. A random sample of 150 books is selected from a much larger number purchased in the last three years. Approximate the probability of (a) Exactly 2 cannot be located. (b) 2 or more cannot be located.

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