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probability statistics

Using And Interpreting Statistics 3rd Edition Eric W. Corty - Solutions

6. The number of complaints that a discount store receives on their product per week is a random variable having Poisson distribution with λ = 5. Find the probability that during any given period of two weeks it will receive: (a) at least 10, (b) exactly nine, (c) at most 12.
5. Based on past records, a retail store manager knows that on average, 30 customers per hour come to the store. Find the probability that in a given five-minute period:(a) At least two will come to the store(b) Exactly four will come to the store(c) At most six will come to the store
4. The probability that a woman will die from breast or cervical cancer is 0.00027. Find the probability that of the 10,000 women who are monitored for breast or cervical cancer: (a) three will die from breast or cervical cancer, (b) at most four will die from breast or cervical cancer, or (c) at
3. The number of defective parts produced per shift can be modeled using a random variable that has the Poisson distribution. Assume that, on average, three defective parts per shift are produced.(a) What is the probability that exactly four defective parts are produced in a given shift?(b) What is
2. A machine in a manufacturing plant has on the average two breakdowns per month.Find the probability that during the next three months it has (a) at least five breakdowns, (b) at most eight breakdowns, (c) more than five breakdowns.
1. A random variable X is distributed as Poisson distribution with λ = 3.5. Use this Poisson distribution (Table A.3) to determine the following probabilities: (a)P(X 7), (d) P(X ≥ 5).
7. It is believed that the probability of auditing a tax return by the IRS depends on the gross income. Suppose that these probabilities are 0.15, 0.18, 0.27, and 0.40 for the tax returns being audited if their gross incomes are $100K or less, more than $100K but less than $250K, more than $250K
6. A regular die is rolled 12 times. What is the probability of getting two threes, four ones, and three fives?
5. A computer store receives flash drives in shipments consisting of four different memories.A particular shipment contains 100 flash drives of which 30% are of 1 GB, 25%of 2 GB, 25% of 8 GB, and the remaining 20% are of 16 GB memory. A random sample of 20 flash drives is selected from that
4. An urn contains six red, eight green, and 11 yellow marbles. A random sample drawn with replacement of 20 marbles is taken. What is the probability that of the 20 marbles seven are red, six green, and seven are yellow.
3. The quality control department of a company has determined that shipments from a certain supplier find four, six, seven, or nine defective items with probabilities 0.55, 0.20, 0.15, and 0.10, respectively. What is the probability that in the next 10 shipments they will find four defective items
2. The records of a cardiology department of a hospital show that patients after their bypass surgery remain in the hospital for five, seven, or 10 days with probability 0.45, 0.35, and 0.20, respectively. What is the probability that of the next 25 patients who go through bypass surgery, 10 will
1. In a certain city, too many accidents occur every year, so the motor vehicle department has been quite strict about passing or failing the persons who take their driving test. The probabilities that a person who takes this test will pass in the first, second, or third attempt are 0.25, 0.30, and
10. It has been claimed that at least 40% of all the personal bankruptcies in the United States are due to medical bills. If in a given county, 10 personal bankruptcies occur during a certain period, then find the probability that at least four of these bankruptcies are due to the medical bills.
9. An electronic system is designed to work as long as at least five of its eight major components function. Each of these components work independently with probability 0.6. What is the probability that the system will work?
8. In a survey conducted by a social worker, 30% of the women responded that they were the victims of domestic violence. Assume that this percentage is true for all 146 4 Discrete Random Variables and Some Important Discrete Probability Distributions women in the United States. Using the binomial
7. In Problem 5, clearly state the probability distribution of the binomial random variable X. What is the probability that the random variable X falls in the interval[μ − 3σ, μ + 3σ]?
6. A multiple choice test consists of 12 questions with each question having three choices. If a student checks the answers randomly, find the probability that the student gets (a) five correct answers, (b) between four and eight (inclusive) correct answers, (c) at most five correct answers.
5. The mean and the variance of a binomial distribution with parameters n and p are 12 and 3. Find the following probabilities: (a) P(X
4. Six missiles are fired at a certain target. The probability that a missile will hit the target is 75%. What is the probability that of the six missiles fired (a) exactly five will hit the target, (b) at least three will hit the target, (c) all six will hit the target?
3. Define Bernoulli trials in words. Suppose that the probability of success of a Bernoulli trial is p, and you are interested in determining the probability of X successes in n independent Bernoulli trials. Describe the probability distribution of the random variable X.
2. Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day 10 patients are admitted and X denotes the number of patients diagnosed with this type of cancer.Determine the probability distribution of the random
1. A sample of 16 PCV valves for gas engines is randomly selected from a very large batch and tested. Let X denote the number of valves out of the 16 selected that are found defective when tested. Valves are defective or nondefective independently. If the probability of a valve being defective is
10. An electronic company ships a lot of 50 computer hard drives to a store. At the arrival of the shipment, the store manager selects at random three hard drives to test. If the lot had five defective hard drives, find the probability that the number of defective hard drives among the three
9. A movie store has five fiction and seven other movies on display. A customer selects four of these 12 at random. What is the probability that the number of fiction movies among the four selected movies is (a) exactly two, (b) between two and four (inclusive), (c) at most two.
8. An IRS inspector randomly selects five persons from a group of 20 who are potential candidates to be audited. Of the 20 persons, nine were audited in the past, while the other 11 have never been audited before. Find the probability that the number of persons selected who were audited in the past
7. A manager of a manufacturing company has 8 female and 12 male engineers in her department. The manager randomly selected a team of six engineers to attend a business meeting. Find the probability that the team had (a) two female engineers and (b) at least three female engineers.4.5 The Bernoulli
6. Referring to Problem 5, let a random variable X denote the number observed. Find the probability distribution of the random variable X and determine the mean and the variance of the distribution you obtained.
5. Twenty identical chips marked as 1, 2, . . . , 20 are put in a container and mixed well. A chip is drawn randomly and the number on the chip is observed. Find the following probabilities that the observed number is (a) greater than 15, (b) between 10 and 18 (inclusive), (c) less than 10.
4. A shipment contains 20 assembled circuit boards of which five are defective. Ten circuit boards from the shipment are selected without replacement. Suppose that X denotes the number of defective boards out of the 10 selected. Find the probability distribution of the random variable X and then
3. Suppose that the random variable X has a hypergeometric distribution with N = 12, n = 4, and N1 = 6. Determine the probability distribution of the random variable X and then find its mean and variance.
2. Suppose that the probability distribution of a random variable X is as shown below.Determine the mean and variance of the random variable Y = 3X.X = x 1 2 3 4 5 6 7 8 p(x) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125
1. A box contains 10 chips numbered from 1 to 10. A chip is selected (with replacement)randomly and the number on that chip is jotted down. Let this number be denoted by a random variable X. Determine the probability distribution of X and then find its mean and variance.
10. Suppose that the moment-generating function of a random variable X is given by MX(t) = (0.3et + 0.7)10 Find the moment-generating function of a random variable (a) Y = 2X and (b)Y = 3X + 5.136 4 Discrete Random Variables and Some Important Discrete Probability Distributions
9. Refer to Problem 7. Find the mean and the variance of the random variable (a)Y = 3X and (b) Y = 2X + 5.
8. A company developed a new shampoo to reduce dandruff. Six persons tried that shampoo. Assume that the probability that a person gets some relief is 0.60. Let X be the number of persons out of the six who find some relief. Determine the probability distribution of the random variable X and then
7. A pair of fair dice is rolled and a random variable X, the sum of points that turn up, is observed. Find the probability distribution of the random variable X and determine the mean and the variance of the distribution you obtained.
6. Suppose that the moment-generating function of a random variable X is given by MX(t) = (0.4et + 0.6)10 Determine the mean and variance of the random variable X.
5. Refer to Problem 4. Find the mean and the variance of the random variable X.
4. A manufacturer of car parts ships five exhaust gas temperature sensors, each of which is independently declared to be either conforming or not conforming. Assume that the probability that a sensor is conforming is 0.75. Let X be the number of sensors of the five shipped that are conforming. Find
3. Each of the following tables lists the values of a random variable X and presumably their corresponding probabilities. Determine whether or not each represents a probability distribution. Justify your answer.(a) .X = x 1 2 3 4 5 p(x) 0.12 0.17 0.31 0.23 0.17(b) .X = x 0 1 2 4 p(x) 0.15 0.15 0.33
2. Each of the following tables lists the values of a random variable X and presumably their corresponding probabilities. Determine whether or not each represents a probability distribution. Justify your answer.(a) .X = x 2 3 4 5 p(x) 0.15 0.25 0.35 0.45(b) .X = x 4 7 8 9 p(x) 0.15 0.15 0.45 0.30
1. A hospital is known for coronary artery bypass grafting. Let X be the number of such surgeries done on a given day. The following table gives the probability distribution of the random variable X:X = x 0 1 2 3 4 5 p(x) 0.02 0.05 0.10 0.15 0.18 0.50 Find the following probabilities:(a) P(X ≤
Given the results of a one-way, repeated-measures ANOVA in APA format, F(3, 36) = 12.56, p < .05, interpret them based only
Given α = .05 and the information in this summary table, (a) write the results in APA format, and (b) state if the results are statistically significant or not: Source of Variability Subjects Treatment Residual Total Sum of Squares Degrees of Freedom Mean Square F ratio 120.00 21 32.00 2 16.00
Given α = .05 and the information in this summary table, (a) write the results in APA format, and (b) state if the results are statistically significant or not: Source of Variability Sum of Squares Degrees of Freedom Mean Square Fratio Subjects 88.00 9 Treatment 60.00 2 30.00 11.24 Residual 48.00
If Fcv — 2.310 and F — 1.96, was H0 rejected?
If Fcv = 3.259 and F — 3.259, was H0 rejected?
Given the following, complete an ANOVA summary table for a one-way, repeated-measures ANOVA: dfSubject 19, dfTreatment= 3, dfResidual = 57, dfTotal — 79, SSSubjects — 101.27, SSTreatment =99.81, SSResidual = 957.48. and SSTotal = 1,158.56.
Given the following, complete an ANOVA summary table for a one-way, repeated-measures ANOVA: dfSubject= 11, dfTreatment= 2, dfResidual= 22, dfTotal= 35, SSSubject= 137.50, SSTreatment= 48.48, SSResidual= 115.50, and ssTotal = 301.48.
If dfTreatment= 2 and dfResidual= 76, state the decision rul?
Given dfTreatment= 3 and dfResidul= 36, (a) what is Fcv? (b) Draw the sampling distribution of F, being sure to label the common zone, the rare zone, and Fcv.
Given dfTreatment= 2 and dfResidual= 10, (a) what is Fcv? (b) Draw the sampling distribution of F, being sure to label the common zone, the rare zone, and Fcv.
If k = 4 and n = 15, what are dfSubject, dfTreatment, dfResidual, and dfTotal?
If k = 3, n = 8, and N = 24, what are dfSubject, dfTreatment, dfResidual, and dfTotal?
a. What is the null hypothesis for Exercise 11.64?b. What is the alternative hypothesis for Exercise 11.64?
a. What is the null hypothesis for a one-way, repeated-measures ANOVA?b. What is the alternative hypothesis for a one-way, repeatedmeasures ANOVA?
The dean of retention at a college wanted to find out if academic problems or social problems caused students to drop out at her college. She took a random sample of first-year students at her college and, on the basis of SAT scores, matched them into groups of three. One member of each group was
The ___ a post-hoc test for use with oneway, repeated-measures ANOVA.
A researcher ends up suggesting replication of study with a larger sample size. The null hypothesis probably was / was not rejected.
If one knows SSSUbject, SSTreatment, and SSResidual, one can calculate SS ___.
After dfSubjectand dfTreatmentare removed from dfTotal what is left is called ___.
if one adds together dfSubject, dfTrearment, and df residual, this equals ___.
When comparing the means of two dependent samples, the author advocates using ___, not ___.
If r 2is calculated for a paired-samples t test, it will over /underestimate the effect size.
Because variability due to subjects is removed from within-groups variability in repeated-measures ANOVA, the numerator/denominator of the F ratio is smaller than it is in between-subjects, one-way ANOVA.
What is called the between-groups effect in between-subjects, oneway ANOVA is called the ___effect in repeated-measures ANOVA.
Because a repeated-measures ANOVA is more ___than a betweensubjects, oneway ANOVA, there is a ___likelihood of being able to reject the null hypothesis.
In repeated-measures ANOVA, the cases should be in the ___order in each cell.
The data used in repeated-measures ANOVA are arranged with cases on ___and levels of the explanatory variable in ___.
A software designer was curious as to how comfort with technology varied across generations. He obtained 10 families and brought in a teenager, a parent, and a grandparent from each family. Then he had each of them, individually, install a new piece of software. For each one, he timed how long it
Given k = 5, n = 16, MSResidual= 12.98, and α = .05, (a) find q and (b)calculate Tukey’s HSD.
Given SSTratment= 35.76 and SSTotal= 124.64, (a) calculate η2. (b) Is this considered a small, medium, or large effect?
Given Fcv = 2.866, dfTreatment= 3, dfResidual= 36, F = 4.36, and α =.05, (a) write the results in APA format. (b) Are the results statistically significant?
Given SSSubject= 123.00, SSTreatment= 216.00, SSResidual= 410.40, SSTotal= 749.40, dfSubject=19, dfTreatment= 3, dfResidual= 57, and dfTotal= 79, complete a one-way, repeated-measures ANOVA summary table.
If dfTreatment= 3, dfResidual= 21, and α = .05, what is the decision rule?
There’s a sample of 12 cases that is measured on an interval-level variable at four points in time. The data will be analyzed with a oneway, repeated-measures ANOVA.a. What are the numerator degrees of freedom for the F ratio?b. What are the denominator degrees of freedom for the F ratio?
State the hypotheses for a one-way, repeated-measures ANOVA.
List the assumptions for a one-way, repeated-measures ANOVA.
What test should be used to analyze these two studies? Select from the single-sample z test; single-sample t test; independent-samples t test; paired-samples t test; between-subjects, one-way ANOVA; and one-way, repeated-measures ANOVA.a. High school seniors who plan to (i) not go to college, (ii)
When comparing the means of two dependent samples, what test should be used? Why?
Into what two factors does one-way, repeated-measures ANOVA divide variability in a set of scores?
When is repeated-measures ANOVA used?
A consumer researcher gave consumers a sample shampoo. After using the shampoo, each consumer used an interval-level scale to rate his or her satisfaction with it. Scores could range from 0 to 100, with higher scores indicating greater satisfaction. Consumers didn’t know each other and were
A sleep specialist investigated the impact of watching TV and using computers, before bedtime, on sleep onset. He obtained 30 college student volunteers and randomly assigned them to three equally sized groups: (1) work on a computer for 30 minutes before going to bed, (2) watch TV for 30 minutes
An addictions researcher was curious about which drug was hardest to quit: alcohol, cigarettes, or heroin. She obtained samples of alcoholics, smokers, and heroin addicts who were in treatment for the second time and found out how long they had remained abstinent, in months, after their first
Given this ANOVA summary table, write the results in APA format using α = .05. (Use dfBetween and dfWithin to find F in order to determine if the null hypothesis was rejected.) Source of Variability Sum of Squares Degrees of Freedom Mean Square Fratio Between groups 42.34 2 21.17 2.23 Within
Given this ANOVA summary table, write the results in APA format using a = .05. (Use dfBetween and dfWithin to find Fcv in order to determine if the null hypothesis was rejected.)
If SSWithween = 168.43 and SSBetween = 764.13, what is SSTotal?
If SSTotal = 98.75 and SSBetween = 40.33, what is SSWithin?
Given the data in this table, calculate SSTotal SSBetween, and SSWithin
Given the data in this table, calculate SSTotal SSBetween, and SSWithin Group 1 Group 2 Group 3 X x X x X x2 112 12,544 98 9,604 88 7,744 104 10,816 90 8,100 85 7,225 88 7,744 76 5,776 80 X Grand x 216.00 23,360.00 276.00 25,448.00 329.00 27,145.00 821.00 75,953.00 n 2 3 4 9
Prepare the data table for use by computational formulas for sums of squares. Group 1 46 Group 2 54 Group 3 74 48 58 80
Prepare the data table for use by computational formulas for sums of squares. Group 1 Group 2 Group 3 108 100 99 102 105 95 91
If dfBetween = 3 and dfWithin = 36, what is Fcv if α = .05?
If dfWithin = 44 and dfBetween = 2, what is Fcv if α = .01?
If n1 = 15, n2 = 12, and n3 = 18, what are (a) dfTotal, (b) dfBetween and (c) dfWithin?Finding Fcv
Write the null and alternative hypotheses for the between-subjects, one-way ANOVA in Exercise 10.74.
Write the null and alternative hypotheses for the between-subjects, one-way ANOVA in Exercise 10.73.
A social psychologist is interested in how people perceive agediscrepant couples. She gets a random sample of shoppers at a mall, has them read a wedding announcement, and then asks them to predict—on an interval-level scale—the newlyweds’ degree of marital happiness after 10 years of

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