- Examine if the following are legitimate probability distributions.a.b.c.d. x -1 234 f(x) 1 243
- For a standard normal random variable Z, find(a) P[Z < 1.56 )(b) P [ Z > 1.245)(c) P[ .61 < Z < 1.92)(d) P [ -1.47 < Z < 1.055)
- In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.Construct a histogram using equal-length intervals starting with (6.5, 6.8 ], where the right-hand
- The stem-and-leaf display shows the final examination scores of 33 students in a geology course. (Leaf unit = 1.0)(a) Find the median score.(b) Find the quartiles. 456700
- A data set has summary statisticsApproximately what proportion of the observations are(a) Below 24.5?(b) Above 4.0?(c) In the interval 7.5-31.5?(d) In the interval 4.0-24.5?(e) In the interval
- 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
- Match the following values of r with the correct diagrams (Figure 8).(a) r = – .3(b) r = .l(c) r = .9Data from in Figure 8 (a) (c) (b)
- The probability distribution of X is given by the functionFind(a) P [ X = 1 ](b) P [ X is odd ] . f(x) 1s (1) 15 for x = 0, 1, 2, 3
- Evaluate:(a)(b)(c)(d)(e)(f) 8 4
- Plot the line y = 4 - 2x by locating the points for x 0 and x = 3. What is its intercept? Its slope?
- Describe a procedure, based on 12 identical cards, that generates an observation from the probability distributionSpecify appropriate numbers, one for each card, that make this probability
- Probabilities, provided by the engaged couple, can help control the number of guests at their wedding. At the planning stage, decisions are necessarily based on the number of persons expected to
- 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
- Suppose the probability distribution of a random variable X has the distributionCalculate the mean and standard deviation of this distribution. f(x) 60 1 77 x for x = 2, 3, 4, 5
- In bidding for a contract to cater a large wedding, a caterer expects she will have a net profit of $3000 if she wins the contract and net loss of $60 if her bid fails. If the probability of getting
- A jar contains 20 pieces of wrapped hard candies, 7 are raspberry, 10 are butterscotch, and 3 are other flavors. Consider 4 successive draws of l piece of candy taken at random from the jar. Suppose
- Refer to Exercise 5.43 but instead assume that the jar contains 2000 pieces of wrapped hard candies, of which 700 are raspberry, 1000 are butterscotch , and 300 are other flavors. Repeat parts
- A backpacking party carries three emergency signal flares, each of which lights with a probability of .94. Assuming that the flares operate independently, find:(a) The probability that at least one
- According to a recent survey, about 40% of adults reported that the most helpful method to achieve a goal is to share their goal with friends and ask them for support. Let S be the event that an
- According to the U.S. Census Bureau, about 10% of persons between 25 and 29 years old live alone. For a random sample of size n, use the binomial table, or software, to find the probability of(a) 1
- Referring to Exercise 5.71, find:(a) The expected number of college seniors, in a random sample of 20, supporting the increased funding.(b) The probability that the number of sampled college seniors
- According to a recent Federal Trade Commission Report, about .13% of the persons in the 20-29 year old age group filed identity theft complaints. From a random sample of n = 600 persons 20-29 years
- John and two of his friends have one-on-one basketball tournaments almost every week. Each person plays each other p erson once. Let X be the number of games that John wins next week X. Based on the
- Refer to Exercise 5.88 but now suppose the sampling is done in two stages: First a list is selected at random and then, from that list, two persons are selected at random without replacement. Let Y
- A student buys a lottery ticket for $2. The prize is a bicycle worth $500. The winning ticket will be chosen at random from 2000 tickets that were sold.(a) What is the probability that the student
- Determine the following probabilities from the curve ∫(x) diagrammed in Exercise 6.1 (a).(a) P( 0 < X < .2)(b) P(1.8 < X < 2.0)(c) P(.4 < X < .6)Data from in Exercise 6.1Which of
- If in three Bernoulli trials the probability that the first two trials are both failures is ¼, what is the probability that the first two are successes and the third is a failure?
- The proportion of people having the blood type O-positive in a large southern city is .38. For two randomly selected donors:(a) Find the probability of at least one type 0 .(b) Find the expected
- 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.
- Two pieces of wood need to be glued together. After applying glue to both pieces, they must be clamped to obtain the best results. The required clamping time in any application is a random variable.
- Find the area under the standard normal curve to the left of(a) z = 1.37 (b) z = .34(c) z = -1.61 (d) z = -2.53
- Find the area under the standard normal curve to the left of(a) z = 1.63(b) z = -1.07(c) z = -1.07(d) z = -1.55
- Find the area under the standard normal curve to the right of(a) z = 1.27(b) z = .54(c) z = -1 .63(d) z = -1.325 (interpolate)
- Find the area under the standard normal curve to the right of(a) z = .63(b) z = 2.63(c) z = -1.23(d) z = 1.635 (interpolate)
- Find the area under the standard normal curve over the interval(a) z = -.85 to z = .85(b) z = -1.15 to z = 1.15(c) z = .58 to z = 2.03(d) z = -.845 to z = 1.366 (interpolate)(e) Check all of
- For a standard normal variable, Z, find(a) P(Z < .73)(b) P(Z < -.73)(c) P(Z > 1.42)(d) P(Z > -1.42)(e) P(-1.4 < Z < 2.57)(f) P( .07 < Z < .70 )(g) P(-1.65 < Z < -.45)(h)
- For X having the density in Exercise 6.55. Find (a) P(X > .8) (b) P(.4 ≤ X ≤ .8) (c) P(.4 < X < .8).Data from in Exercise 6.55Determine (a) the median and (b) the
- Find(a) P(Z < .14)(b) The 14th percentile of Z(c) P(Z < .86)(d) The 86th percentile of Z.
- 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:X = 11 6 ≤ X ≤ 12 6 < X < 12(b)
- The bell-shaped histogram for the heights of three-year-old red pine seedlings on shown below is consistent with the assumption of a normal distribution having mean = 280 and sd = 58 millimeters. Let
- If X has a normal distribution with μ = 90 and σ = 4, find b such that(a) P(X < b) = .6700(b) P(X > b) = .0110(c) P(IX - 90 | < b) = .966(d) Check all of your answers using software.
- The population density function and that for the sampling distribution of X̅, for n = 2, are shown in Figure 6. Identify which one is the sampling distribution and explain your answer.
- 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 X̅ and s2 for each .(b) Determine the sampling distribution of
- Refer to the data on earthquakes of magnitude greater than 6.5 in Exercise 2.20. The data suggests that one plausible model, for X = magnitude, is a population distribution having mean μ = 7 .05 and
- 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
- A population has distributionLet 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 X̅ =
- Using the sampling distribution determined for X̅ = (X1 + X2) / 2 in Exercise 7.4, verify that E [X̅] = μ and sd(X̅) = σ/ √2.Data from in Exercise 7.4From the set of numbers { 3, 5, 7 }, a
- 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 X̅ = 43 and s = 7. 7 days for the time
- When estimating μ from a large sample, suppose that one has found the 95% error margin of X̅ to be 10.4. From this information, determine:(a) The estimated S.E. of X̅.(b) The 90% error margin.
- 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
- A nutritionist records the time to eat an evening meal, at a student cafeteria, for 64 students. She obtains X̅ = 36.2 and s = 5.6 minutes and reports that the 95% confidence interval for the mean
- 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
- 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 X̅ = 43 and s = 7.7 days for the time
- 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 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 X̅ = 43 and s = 7. 7 days for the time
- 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
- 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 and later released into the wild.
- Given here are the observed sample proportions p̂ 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
- 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
- Use software to find(a) T < -1.729 when d.f. = 19.(b) ITI > 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 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.
- Use software to find the probability(a) T ≤ –1.3 when d.f. = 12.(b) T > l.7 when d.f. = 21.(c) ITI > l.35 when d.f. = 33.(d) Find c such that P[T > c] = .015 when d.f. = 18.(e) Find c
- 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
- 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)
- Refer to Exercise 9.12. Do these data support the claim that the mean monthly rent for a two-bedroom apartment differs from 1200 dollars? Take a = .05.Data from in Exercise 9.12The monthly rent
- 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 =
- Ten participants tried a new weight loss diet for two months. The resulting weight losses (pounds} are20.2 11.0 15.4 9 .9 7.9 15.6 15.5 23.1
- 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 in Exercise 9.41Plastic sheets produced by a
- Using the t able for the χ2 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
- Use software to find the probability(a) χ2 ≤ 17.2 when d.f. = 9.(b) χ2 > 13.7 when d.f. = 23.(c) Find c such that P(χ2 > c) = .015 when d.f. = 12.(d) Find c such that P(χ2 < c) = .04
- Referring to Exercise 9.21 , construct a 95% confidence interval for the population standard deviation of the diameters of Indian mounds.Data from in Exercise 9.21The following measurements of the
- 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 in Exercise 9.22Measurements of the
- Determine a 99% confidence interval for μ using the data in Exercise 9.49.Data from in Exercise 9.49Measurements of the amount of suspended solids in river water on 14 Monday mornings yield x̅ = 47
- Referring to Exercise 9 .55, test H0 : μ = 2.8 versus H1 : μ ≠ 2.8 using a = .02.Data from in Exercise 9 .55In a study of head injuries to ice hockey players the number of hits were
- Use software to find(a) χ2.05 with d.f. = 3 .(b) χ2.025 with d.f. = 24.(c) The lower .05 point with d.f. = 7.(d) The lower .025 point with d.f. = 32.
- Use software to find(a) The 90th percentile of χ2 when d.f. = 13.(b) The 10th percentile of χ2 when d.f. = 4.(c) The median of χ2 when d.f. = 32.(d) The 1st percentile of χ2 when d.f. = 46.
- Refer t o the data of Exercise 9.60. Is there strong evidence that the standard deviation for the efficiency of the new model is below 3.0?Data from in Exercise 9.60Combustion efficiency measurements
- 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
- 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
- One semester, an instructor taught the same computer course at two universities located in different cities. He was able to give the same final at both locations. The student's scores provided the
- 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
- According to the assumptions underlying the two independent samples design, let the first population be N (5, 3) and the second be N (9, 6). Identify the values of the parameters μ1, σ1, μ2, σ2.
- 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) .R: t.test(x,y) after x=c(
- Given the following matched pairs sample,(a) Evaluate the t statistic(b) How many degrees of freedom does this t have? x T9 487 y 546232
- Randomly allocate 2 subjects from among Al, Bob, Carol, Ellen, John to be in the control group. The others will receive a treatment.
- Randomly allocate three subjects from among 6 mice, Alpha, Tau, Omega, Pi, Beta, Phi to group 1.
- Two sun blockers are to b e 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
- An experiment was conducted to study whether cloud seeding reduces the occurrences of h ail. At a hail-prone geographical area, seeding was done on 50 stormy days and another 155 stormy days were
- 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 p air are matched
- A study (courtesy of R. Golubjatnikov) is undertaken to compare the rates of prevalence of CF antibody to parainfluenza I virus among boys and girls in the age group 5 to 9 years. Among 113 boys
- Consider the following linear regression modelwhere β0 = 4, β1 3, and the normal random variable e has the standard deviation 4.(a) What is the mean of the response Y when x = 4? When x =
- Identify the values of the parameters β0, β1, and σ in the statistical modelY = -3 + 4x + ewhere e is a normal random variable with mean 0 and standard deviation 2.
- A help desk devoted to student software problems also receives phone calls. The number of persons that can be served in person, within one hour, is the response y . The predictor variable, x, is the
- Consider the linear regression modely = β0 + β1x + ewhere β0 = -2, β1 = -1, and the normal random variable e has standard deviation 3.(a) What is the mean of the response Y when x = 3? When X =
- A student hourly employee does small secret arial projects.The number of projects she completes in a day is the response variable y . The number of hours she works in a day is the predictor variable
- Using the formulas of β̂1 and SSE, show that SSE can also be expressed as(a)(b) SSE = S..... yy B₁ Sxv xy
- An engineer found that by adding small amounts of a compound to rechargeable batteries during manufacture, she could extend their lifetimes. She experimented with different amounts of the additive (
- One measure of the development of a country is the Human Development Index (HDI). Life expectancy, literacy, educational attainment, and gross domestic product per capita are combined into an index
- Referring to the formulas of β̂0 and β̂1 , show that the point (x̅, y̅) lies on the fitted regression line.
- (a) Show that the sample correlation coefficient rand the slope Pi of the fitted regression line are related as(b) Show that SSE = (1 -r2) Syy· r || BI√Sxx XX IS..... yy