# 1) The table lists the smoking habits of a group of college students. Answer: 0.218

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2 ) A game has three outcomes. The probability of a win is 0., the probability of tie is 0.5, and the probability of a loss is 0.. What is the probability of not winning in a single play of the game. Answer: 0.6 8) A human gene carries a certain disease from the mother to the child with a probability rate of %. That is, there is a % chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. Answer: ) A human gene carries a certain disease from the mother to the child with a probability rate of 9%. That is, there is a 9% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has five children. Assume that the infections of the five children are independent of one another. Find the probability that at least one of the children get the disease from their mother. Answer: ) In how many ways can a committee of three men and four women be formed from a group of 0 men and 0 women? Answer: ) How many distinct arrangements can be formed from all the letters of "statistics"? Answer: 50,00 2) Given the sets of digits {,,, 6, 8}, how many different numbers between 0,000 and 80,000 can be written using these digits if repetition of digits is allowed? Answer: 250 ) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last. Answer: 20; 2; 0 ) From 8 names on a ballot, a committee of will be elected to attend a political national convention. How many different committees are possible? Answer: 56 5) The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. x P(x) Answer: mean:.8; standard deviation:.0 2

5 ) A random sample of 0 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. \$.60 \$.50 \$2.80 \$6.0 \$2.60 \$5.20 \$6.5 \$.25 \$8.00 \$.00 Find the 95% confidence interval for the true mean. Answer: (\$.9, \$6.0) 8) The grade point averages for 0 randomly selected high school students are listed below. Assume the grade point averages are normally distributed Find a 98% confidence interval for the true mean. Answer: (.55,.5) 9) Suppose you are using = 0.05 to test the claim that µ 2 using a P-value. You are given the sample statistics n = 5, x =., and = 2.. Find the P-value. Answer: ) Given H0: µ = 25, H: µ 25, and P = Do you reject or fail to reject H0 at the 0.0 level of significance? Answer: fail to reject H0 ) Given H0: µ 8, H: µ < 8, and P = Do you reject or fail to reject H0 at the 0.05 level of significance? Answer: fail to reject H0 2) A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5. A random sample of 0 teachers provided the data below. At = 0.05, test the district's claim using P-values Answer: P-value = , P <, reject H0; There is sufficient evidence to support the school district's claim. 5

6 Provide an appropriate response. ) Construct a scatter plot for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. x y Answer: There appears to be no linear correlation. ) Calculate the correlation coefficient, r, for the data below. x y Answer: ) The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Calculate the correlation coefficient r. Gestation, x Life span, y Answer: ) In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam. Calculate the correlation coefficient, r. Number of years, x Grades on test, y Answer: 0.9 ) Given a sample with r = -0.5, n = 20, and = 0.0, determine the standardized test statistic t necessary to test the claim = 0. Round answers to three decimal places. Answer:.29 6

7 8) Given a sample with r = -0.65, n = 22, and = 0.02, determine the standardized test statistic t necessary to test the claim = 0. Round answers to three decimal places. Answer: ) For the data below, test the significance of the correlation coefficient using = 0.0 and the claim = 0. x y Answer: critical value t0 = ±.860; standardized test statistic t 0.296; fail to reject H0; There is not sufficient evidence to conclude that a significant correlation exists. 50) Given a sample with r = -0.5, n = 20, and = 0.0, determine the critical values t0 necessary to test the claim = 0. Answer: ± ) Find the equation of the regression line for the given data. x y Answer: y = 2.09x ) The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Find the equation of the regression line for the given data. Gestation, x Life span, y Answer: y =.52x ) A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. Miles traveled, x Sales, y ) 55) Answer: y =.529x +.96 Given the equation of a regression line is y =.5x - 5., what is the best predicted value for y given x = -.2? Assume that the variables x and y have a significant correlation. Answer: -9.6 Given the equation of a regression line is y = -.5x-., what is the best predicted value for y given x = 9.5? Assume that the variables x and y have a significant correlation. Answer: -6.5

8 use alpha.05 the given data to find the best predicted value of the response variable. 56) The regression equation relating dexterity scores (x) and productivity scores (y) for the employees of a company is y = x. Ten pairs of data were used to obtain the equation. The same data yield r = and y = 56.. What is the best predicted productivity score for a person whose dexterity score is 2? 5) 58) Answer: Six pairs of data yield r = 0. and the regression equation y = 5x + 2. Also, y = 8.. What is the best predicted value of y for x = 5? Answer: 8. Nine pairs of data yield r = 0.86 and the regression equation y = x. Also, y = 6.. What is the best predicted value of y for x = 50? Answer:

9 Answer Key Testname: FINAL_EXAM_REVIEW ) ) 0.5 ) No ) ) 0.5 6) 2 ) 0.6 8) ) ) ) 50,00 2) 250 ) 20; 2; 0 ) 56 5) mean:.8; standard deviation:.0 6) 0.02 ) ) ) 5 20) mean: 9.; standard deviation: ) ) ) 0.5 2) ) 5.98%, 6.02% 26) 9.85% 2).00 28) ) 0.6 0) ) (0.8, 0.50) 2). ±.05 ).5625 ±.029 ) (2.5,.2) 5) 8 ± 2.262(.0/ 0) 6) (.29, 85.) ) (\$.9, \$6.0) 8) (.55,.5) 9) ) fail to reject H0 ) fail to reject H0 2) P-value = , P <, reject H0; There is sufficient evidence to support the school district's claim. 9

10 Answer Key Testname: FINAL_EXAM_REVIEW ) There appears to be no linear correlation. ) ) ) 0.9 ).29 8) ) critical value t0 = ±.860; standardized test statistic t 0.296; fail to reject H0; There is not sufficient evidence to conclude that a significant correlation exists. 50) ± ) y = 2.09x ) y =.52x ) y =.529x ) ) ) ) 8. 58)

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