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theory of statistics

Questions and Answers of Theory of Statistics

Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that:a. None of the antennas is defective.b. Three or more of the
The sales of Lexus automobiles in the Detroit area follow a Poisson distribution with a mean of 3 per day.a. What is the probability that no Lexus is sold on a particular day?b. What is the
A manufacturer of computer chips claims that the probability of a defective chip is .002. The manufacturer sells chips in batches of 1000 to major computer companies such as Dell and Gateway.a. How
A recent study conducted by Penn, Shone, and Borland, on behalf of LastMinute.com, revealed that 52 percent of business travelers plan their trips less than two weeks before departure. The study is
Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college stUdents. She believes 45 percent of college students watch soap operas during the afternoon. To further
Recent statistics suggest that 15 percent of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 "hits"
The Bank of Hawaii reports that 7 percent of its credit card holders will default at some time in their life. The Hilo branch just mailed out 12 new cards today.a. How many of these new cardholders
A federal study reported that 7.5 percent of the U.S. workforce has a drug problem. A drug enforcement official for the State of Indiana wished to investigate this statement. In his sample of 20
Tire and Auto Supply is considering a 2-for-1 stock split. Before the transaction is finalized, at least two-thirds of the 1,200 company stockholders must approve the proposal. To evaluate the
An auditor for Health Maintenance Services of Georgia reports 40 percent of the policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company
Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Span ish-speaking American.Of the first 12 potential
A recent survey reported that the average American adult eats ice cream 28 times per year.The same survey indicated 33 percent of the respondents said vanilla was their favorite flavor of ice cream.
Croissant Bakery, Inc. offers special decorated cakes for birthdays, weddings, and other occasions. They also have regular cakes available in their bakery. The following table gives the total number
The vice president of human resources. at Lowes is studying the number of on-the-job accidents over a period of one month. He developed the following probability distribution. Compute the mean,
Seaside Villas, Inc. has a large number of villas available to rent each month. A concern of management is the number of vacant villas each month. A recent study revealed the percent of the time that
For each of the following indicate whether the random variable is discrete or continuous.a. The length of time to get a haircut.b. The number of cars a jogger passes each morning while running.c. The
What is the difference between a random variable and a probability distribution?[6-6]
Textbook authors and publishers work very hard to minimize the number of errors in a text.However, some errors are unavoidable. Mr. J. A. Carmen, statistics editor, reports that the mean number of
It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc. will receive a busy signal. What is the probability that of today's 1,200 callers at least 5 received
Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan.
In a Poisson distribution J.L = 4.a. What is the probability that x = 2?b. What is the probability that x ::;; 2?c. What is the probability that x > 2?
In a Poisson distribution J.L = 0.4.a. What is the probability that x = O?b. What is the probability that x > O?
Steele Electronics, Inc. sells expensive brands of stereo equipment in several shopping malls throughout the northwest section of the United States. The Marketing Research De- .partment of Steele
The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports they can resolve customer problems the same day they are reported in 70
A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a
In a recent study 90 percent of the homes in the United States were found to have largescreen TVs. In a sample of nine homes, what is the probability that:a. All nine have large-screen TVs?b. Less
In a binomial distribution n = 12 and 'IT = .60. Find the following probabilities.a. x = 5.b. x:s; 5.c. x;:: 6.
In a binomial distribution n = 8 and 'IT = .30. Find the probabilities of the following events.a. X= 2.b. x:s; 2 (the probability that x is equal to or less than 2).c. x;:: 3 (the probability that x
Suppose 60 percent of all people prefer Coke to Pepsi. We select 18 people for further study.a. How many would you expect to prefer Coke?b. What is the probability 10 of those surveyed will prefer
A recent survey by the American Accounting Association revealed 23 percent of students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent
A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:a. The probability of making exactly four sales.b. The
The industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.a. What is the
The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different
An American Society of Investors survey found 30 percent of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability:a. Exactly two of the
Assume a binomial distribution where n = 5 and 'IT = .30.a. Refer to Appendix A, and list the probabilities for values of x from 0 to 5.b. Determine the mean and standard deviation of the
In a binomial situation n = 5 and 'IT = .40. Determine the probabilities of the following events using the binomial formula.a. x = 1b. X= 2
In a binomial situation n = 4 and 'IT = .25. Determine the probabilities of the following events using the binomial formula.a. x = 2b. x = 3
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of
Which of these variables are discrete and which are continuous random variables?a. The number of new accounts established by a salesperson in a year.b. The time between customer arrivals to a bank
Three tables listed below show "random variables" and their "probabilities." However, only one of these is actually a probability distribution.a. Which is it?x P(x) x P(x) x P(x)5 .3 5 .1 5 .5 10 .3
Data Set 5 This data set is discussed in Chapter 8. The study involves 117 persons in 39 matched sets, each strata containing 3 persons, 1 of whom is a case and the other 2 are matched controls. The
Data Set 4 Data set name: agentor.dat These are data from a pair-matched case-control study, where the cases are babies born with genetic anomalies and controls are babies born without such
Data Set 3 Data set name: conf.dat Variable 1 = person id #2 = sodal dass status-SOC 3 = number of times victimized-VICT 4 =AGE 5 = index of confidence in legal system-CONF 1 low 0 4 25 2 low 0 14 45
Data Set 2 Appendix: Computer Data Sets 255 Data set name: bronchitis.dat Variable 1 = number of bronchitis cases-BRC 2 = total number at risk in stratum 38 48 28 40 84 102 47 59 3 = smoking status
Data Set 1 Data set name: evans.dat Variable 1 = number of coronary heart disease cases-CHD 2 = total number at risk in stratum 17 274 15 122 7 59 5 32 1 8 9 39 3 17 14 58 3 = serum catecholamine
18. The following printout results from fitting a no interaction model to the cervical cancer data:Variable ß S.E. Chi sq P SMK 1.4361 0.3167 20.56 0.0000 NS AS 0.9598 0.3057 9.86 0.0017-0.6064
17. When NS = 1, the 95% confidence interval for the adjusted odds ratio for the effect of smoking on cervical cancer status is given by the limits(0.96, 5.44). Use this result and your estimate from
16. Use the formula computed in Question 15 to compute numerical values for the estimated odds ratios when NS = 1 and NS = O.
15. Using the printout, give a formula for the point estimate of the odds ratio for the effect of SMK on cervical cancer status which adjusts for the confounding effects of NS and AS and allows for
14. Based on the printout above, is the product term SMKxNS significant?Explain.
13. State the logit form of the model used in the above printout.
12. Why are the variables age and socioeconomic status missing from the printout given above, even though these were variables matched on in the study design?
11. What method of estimation was used to obtain estimates given in the above printout? Explain.
10. Explain how the confidence interval given in the printout is computed.The following questions consider information obtained from a matched case-contral study of cervical cancer in 313 women from
8. The following printout results from using conditional ML estimation of an appropriate logistic model for analyzing the Agent Orange data:95% CI for OR Variable ß P-value OR L U E 0.032 0.128
7. State the logit form of the logistic model that can be used to analyze the Agent Orange study data.
6. Consider the foIlowing McNemar's table from the "Agent Orange"study analyzed by Donovan et al. (Med. 1. of Australia, 1984). This is a pair-matched case-control study, where the cases are babies
T F 5. In a matched case-control study, logistic regression can be used when it is desired to control for variables involved in the matching as weIl as variables not involved in the matching.
T F 4. McNemar's test statistic is not appropriate when there is R-to-l matching and R is at least 2.
T F 3. If we do not match on an important risk factor for the disease, it is still possible to obtain an unbiased estimate of the odds ratio by doing an appropriate analysis that controls for the
T F 2. An advantage of matching over not matching is that information may be lost when not matching.
T F 1. In a category matched 2-to-l case-control study, each case is matched to two controls who are in the same category as the case for each of the matching factors.
18. For the model used in Exercise 16, describe the strategy you would use to arrive at a final model that controls for confounding and interaction.
15. If unconditional ML estimation had been used instead of conditional ML estimation, what estimate would have been obtained for the odds ratio of interest? Which estimation method is correct,
12. Consider again thc pair-matched case-control data described in Exercise 10 (W = 50, X = 40, Y = 20, Z = 100). Using conditional ML estimation, a logistic model fitted to this data resulted in an
11. For the pair-matched case-control study described in Exereise 10, let E denote the (0, 1) exposure variable and let D denote the (0, 1) disease variable. State the logit form of the logistic
T F 9. When carrying out a Mantel-Haenszel chi-square test for 4-to-1 matched case-control data, the number of strata is equal to five.T F 10. Suppose in a pair-matched case-control study, the number
T F 8. In a pair-matched case-control study, the Mantel-Haenszel odds ratio (i.e., the MOR) is equivalent to McNemar's test statistic (X- Y)2j(X + Y). (Note: X denotes the number of pairs for which
T F 7. A matched analysis can be carried out using a stratified analysis in which the strata consists of the collection of matched sets.
T F 6. When in doubt, it is safer to match than not to match.
T F 5. One reason for deeiding to match is to gain validity in estimating the odds ratio of interest.
T F 4. An advantage of matching over not matching is that a more preeise estimate of the odds ratio may be obtained from matching.
T F 3. In a 3-to-1 matched case-control study, the number of observations in each stratum, assuming sufficient controls are found for each case, is four.
T F 2. In a follow-up study, pair-matching on age is a procedure by which the age distribution of cases (Le., those with the disease)in the study is constrained to be the same as the age distribution
T F 1. In a case-control study, category pair-matching on age and sex is a procedure by which, for each control in the study, a case is found as its pair to be in the same age category and same sex
7. Suppose the variable NS X AS is dropped from the model based on the scenario described in Question 13. Describe how you would assess confounding and precision for any other V terms still eligible
The following questions consider the use of logistic regression on data obtained from a matched case-control study of cervical cancer in 313 women from Sydney, Australia (Brock et al. , 1. Nat.
A prevalence study of predictors of surgical wound infection in 265 hospitals thraughout Australia collected data on 12,742 surgical patients(McLaws et al., Med. J. of Australia, 1988). For each
The following questions consider the use of logistic regression on data obtained from a matched case-control study of cervical cancer in 313 women from Sydney, Australia (Brock et al., J. Nat. Cancer
T F 10. If the variables EXA2 and ExAXB are found to be significant during interaction assessment, then a camplete list of all components of these variables that must remain in any further models
T F 9. A model containing the variables E, A, B, C, A2, AXB, EXA, EXA2, EXAXB, and ExC is hierarchically weIl formulated.
T F 8. During variable specification, the potential effect modifiers should be chosen by considering possible statistical problems that may result from the analysis.
T F 7. During variable specification, the potential effect modifiers should be chosen by considering prior research or theory about the risk factors measured in the study.
T F 6. During variable specification, the potential confounders should be chosen based on analysis of the data under study.
T F 5. Getting a precise estimate takes precedence over getting an unbiased answer.
T F 4. The assessment of confounding may involve statistical testing.
T F 3. The assessment of interaction may involve statistical testing.
T F 2. The assessment of interaction should precedc thc asscssment of confounding.
T F 1. The three stages of the modeling strategy described in this chapter are interaction assessment, confounding assessment, and precision assessment.
9. Suppose the interaction assessment stage for the model of Example 3 finds the following two-factor product terms to be significant: HT X CT and HT X SEX; the other two-factor product terms are not
6. Suppose for the model described in Exercise 3 that a Wald test is carried out for the significance of the two-factor product term HT X AGE. Is this test dependent on coding? Explain briefly.
5. Suppose for the model described in Exercise 4, that a Wald test is carried out for the significance of the three-factor product term HT X AGE X SEX. Explain what is meant by the statement that the
4. Suppose the product term HT x AGE x SEX is added to the model described in Exercise 3. Is this new model still hierarchically weIl formulated?If so, state why; if not, state why not.
3. State the logit form of a hierarchically well-formulated E, V, W model for the above situation in which the Vs and the Ws are the C's themselves.Why is this model hierarchicaIly weIl formulated?
2. In defining an E, V, W model to describe the effect of HT on the development of surgical wound infection, describe how you would determine the W variables to go into the model. (In answering this
A prevalence study oE predictors of surgical wound inEection in 265 hospitals throughout Australia collected data on 12,742 surgical patients (McLaws ct al., Med. J. of Australia, 1988). For each
8. Use the formula for the adjusted odds ratio in Question 7 to compute numerical values for the estimated odds ratios when NS = 1 and when NS = O.
6. Carry out the Wald test for the effect of SMK X NS, controlling for the other variables in model II. In carrying out this test, provide the same information as requested in Ouestion 3. Is the test
5. Now consider model II: Carry out the likelihood ratio test for the effect of the product term SMK X NS on the outcome, controlling for the other variables in the model. Make sure to state the null
3. For model I, test the hypothesis for the effect of SMK on cervical cancer status. State the null hypo thesis in terms of an odds ratio parameter, give the forrnula for the test statistic, state

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