Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) = 0.20 and P(B) = 0.50. (There are various packages such as Minitab, SPSS, SAS, JMP, and R.) (a) Why is it not the case that P(A) + P(B) = 1? O The probabilities should add to 1; P(A) or P(B) must be recorded incorrectly. O The probabilities do add to 1. O The probabilities do not add to 1 because there are other software packages for which requests could be made. O The probabilities are not mutually exclusive and thus they do not need to add to 1. O The probabilities do not add to 1 because they are independent events. (b) Calculate P(A'). (c) Calculate P(A U B). (d) Calculate P(A' n B').

Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) = 0.20 and P(B) = 0.50. (There are various packages such as Minitab, SPSS, SAS, JMP, and R.) (a) Why is it not the case that P(A) + P(B) = 1? O The probabilities should add to 1; P(A) or P(B) must be recorded incorrectly. O The probabilities do add to 1. O The probabilities do not add to 1 because there are other software packages for which requests could be made. O The probabilities are not mutually exclusive and thus they do not need to add to 1. O The probabilities do not add to 1 because they are independent events. (b) Calculate P(A'). (c) Calculate P(A U B). (d) Calculate P(A' n B').

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Two electric generators are connected in series to supply electricity for a company during network system failures. When the electric network fails, generator 1 turns on and supplies electricity until its fuel finishes. If the network electric supply is still off, generator 2 turns on and supplies electricity. Suppose that the time each generator supplies electricity is normally distributed and independent of the other generator. For generator 1 its X₁, Normally distributed with mean 7.00 hours and variance 1.5², [N (7.00, 1.5²)] and for generator 2 its X2, Normally distributed with mean 5.00 hours and variance 1.0², [N(5.00, 1.0²)]. Determine the probability that both generators will provide at least 10 hours of electric supply during a network failure. (Note: You may use the central limit theorem with the fact that T=X₁+X₂ is Normal with mean µ₁+µ2 and variance 0²₁+0²₂). Probability (T210)=
Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 33arrests last month, 25were of males aged 15 to 34 years. Use a 1%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. a. What is the level of significance? answer .01 b.State the null and alternate hypotheses. Which one? Its the third. H0: p< 0 .7; H1: p= 0.7 H0: p≠0.7; H1: p= 0.7 H0: p= 0.7; H1: p≠0.7 H0: p= 0 .7; H1: p< 0.7 H0: p= 0.7; H1: p> 0.7 c. What sampling distribution will you use? Its the last one. The Student's t, since np> 5 and…
Will improving customer service result in higher stock prices for the companies providing the better services? "when a company's satisfaction score has improved over the prior years results and is above the national average (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run." The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer satisfaction index. Assume that the scores are based on a poll of 55 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 7 points in each case. Company year 1 score year 2 score Rite Aid 72 75 Expedia 78 79 J.C Penney 75 77 a. For Rite Aid is the increase in the satisfaction score from year 1 to year 2 statistically significant? use ax=.05 and null…
A researcher investigates whether cold medication effects mental alertness. It is known that scores on a standardized test containing a variety of problem-solving tasks are normally distributed with  = 64 and  = 8. A random sample of n = 16 teenage and a sample of n = 25 adults are given the drug and then tested. On average, the teenagers scored and average of ? = 58 and the adults scored and average of M = 65.5.a. Are the data sufficient to conclude that the medication significantly reduces mental alertness in teenagers? Test with  = .01.b. Are the data sufficient to conclude that the medication significantly increases mental alertness in adults? Test with  = .01.
The Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = II
Consider a within-subjects experimental design with two conditions. The experimenter ran both a correlated t test (which is the correct analysis) and (incorrectly) an independent-groups t test. The experimenter found the correlated t test was significant whereas the independent-groups t test was not. The experimenter concluded that this was because the mean difference score across subjects was greater than the difference between the means of the conditions. Is this the correct conclusion? yes no
3. Let X, X2, .. X5, be a random sample from a population having mean u and variance o?, and let ô, =(x, + X, + X, + X,) and ô, =(2x, + X, + X, - X,) be two estimates of u. * Which of these two estimators is unbiased? * Which is the better estimator, and why? %3D
Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (currently 75.7), studies show its shares have a good chance of outperforming the broad stock market in the long run." The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 67 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case. Company Year 1 Score Year 2 Score Rite Aid 73 75 Expedia 72 75 J.C. Penney 73 74 a. For Rite Aid, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use a = .05 and null hypothesis is Ho : H1 – 42 <0. What can you conclude? z value (to 2 decimals) p-value (to…
Q12
An elementary school claims the variation in reading scores of its fourth grade students is less than o = 3. 25. Determine whether the hypothesis for this claim is left-tailed, right-tailed, or two-tailed. left-tailed right-tailed two-tailed
Which of the following is the research hypothesis of one-tailed dependent t-test expecting to see a significant decrease in the observed scores? A. mean(posttest) < mean(pretest) B. mean(posttest) = mean(pretest) C. mean(posttest) > mean(pretest) D. mean(posttest) ≠ mean(pretest)