# E205 Final: Version B

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1 Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region she use if the population standard deviation σ is known? a. Reject H 0 if z < 2.33 b. Reject H 0 if z < 2.58 c. Reject H 0 if z > 2.33 d. Reject H 0 if z > For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is: a. smaller than 1.96 or greater than 1.96 b. greater than 1.96 or smaller than 1.96 c. smaller than 1.96 or greater than 1.96 d. greater than or less than In a simple linear regression problem, the following sum of squares are produced: (y i y) 2 = 200, (y i y8 i ) 2 = 50, and (y8 i y) 2 = 150. The percentage of the variation in y that is explained by the variation in x is: a. 25% b. 75% c. 33% d. 50% 4. In simple linear regression, most often we perform a two-tail test of the population slope β 1 to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as: a. H 0 : β 1 = 0 b. H 0 : β 1 = b 1 c. H 0 : β From a sample of 400 items, 14 are found to be defective. The point estimate of the population proportion defective will be: a. 14 b c d

2 Name: 6. The rejection region for testing H 0 : µ = 100 vs. H 1 : µ 100, at the 0.05 level of significance is: a. z < 0.95 b. z > 1.96 c. z > 1.65 d. z < If the coefficient of determination is 0.975, then which of the following is true regarding the slope of the regression line? a. All we can tell is that it must be positive. b. It must be c. It must be d. Cannot tell the sign or the value. 8. Suppose an interval estimate for the population mean was to The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: a b c d Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company who makes Kleenex brand tissues thinks that fewer of their tissues are needed. What are their null and alternative hypotheses? a. H 0 : µ = 60 vs. H 1 : µ > 60 b. H 0 : µ = 60 vs. H 1 : µ < 60 c. H 0 : X = 60 vs. H 1 : X < 60 d. H 0 : µ < 60 vs. H 1 : µ = If a test of hypothesis has a Type I error probability of.05, this means that: a. if the null hypothesis is true, we don't reject if 5% of the time. b. if the null hypothesis is true, we reject it 5% of the time. c. if the null hypothesis is false, we don't reject it 5% of the time. d. if the null hypothesis is false, we reject it 5% of the time. 11. Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05? a b c d In the simple linear regression model, the y-intercept represents the: a. change in y per unit change in x. b. change in x per unit change in y. c. value of y when x = 0. d. value of x when y = 0. 2

3 Name: 13. The hypothesis of most interest to the researcher is: a. the alternative hypothesis. b. the null hypothesis. c. both hypotheses are of equal interest. d. Neither hypothesis is of interest. 14. For the following multiple regression model: y8 = 2 3x 1 + 4x 2 + 5x 3, a unit increase in x 1, holding x 2 and x 3 constant, results in: a. an increase of 3 units on average in the value of y. b. a decrease of 3 units on average in the value of y. c. an increase of 8 units in the value of y. 15. If the coefficient of correlation is 0.60, then the coefficient of determination is: a b c d If the lower and upper confidence limits of the population proportion p, using a sample of size 1500, are and 0.238, respectively, then the lower and upper confidence limits of the total number of successes in the population, given that the population size is 750,000, are respectively: a. 276 and 357 b. 137,724 and 178,143 c. 138,000 and 178,500 d. 138,276 and 179, In performing a regression analysis which of the following must be true about the distribution of the error variable? a. The distribution is normal with mean zero. b. The errors associated with one y value are independent of errors associated with another y value. c. The standard deviation is constant for each value of x. d. All of these choices are true. 18. A professor of statistics refutes the claim that the average student spends 3 hours studying for the midterm exam. She thinks they spend more time than that. Which hypotheses are used to test the claim? a. H 0 : µ 3 vs. H 1 : µ > 3 b. H 0 : µ = 3 vs. H 1 : µ 3 c. H 0 : µ 3 vs. H 1 : µ = 3 d. H 0 : µ = 3 vs. H 1 : µ < For the multiple regression model: y8 = x 1 15x x 3, if x 2 were to increase by 5, holding x 1 and x 3 constant, the value of y will: a. increase by 5. b. increase by 75. c. decrease on average by 5. d. decrease on average by 75. 3

4 Name: 20. After calculating the sample size needed to estimate a population proportion to within W=0.04, your statistics professor told you the maximum allowable error must be reduced to just W=0.01. If the original calculation led to a sample size of n=800, the sample size will now have to be: a. 800 b c. 12,800 d A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal: a b c d The coefficient of correlation is used to determine: a. the strength of the linear relationship between x and y. b. the least squares estimates of the regression parameters. c. the predicted value of y for a given value of x. d. All of these choices. 23. Use your results from Model 1,2,3, and 4 to answer these questions. The coefficient estimate on weight for Model 1 is a c b d Use your results from Model 1,2,3, and 4 to answer these questions. According to these data, are women less intelligent than men. a. Yes, according to Model 1 c. No, according to Model 4 b. Yes, according to Model 2 d. No, none of the Models predicts this 25. Use your results from Model 1,2,3, and 4 to answer these questions. Is the size of the brain a predictor for intelligence? a. Yes, at the 1, 5, and 10 % significance c. Yes, at the 10% only significance level level b. Yes, at the 5% and 10% significance level only d. No, it s not a predictor 26. Use your results from Model 1,2,3, and 4 to answer these questions. According to the coefficient of determination, which one is the best model? a. Model 1 c. Model 3 b. Model 2 d. We cannot compare all the models because some have different dependent variables and therefore explain different things 4

5 Name: 27. Use your results from Model 1,2,3, and 4 to answer these questions. Go to Model 4 and calculate the standard deviation of the residuals. Hint: You can find the residual column at the bottom of your regression output, between the Predicted performance IQ column and the Standard Residuals column. What is this standard deviations of the residuals. a c b d Use your results from Model 1,2,3, and 4 to answer these questions. Use Model 1 and predict the full IQ score of a male with size weight height a c b d Use your results from Model 1,2,3, and 4 to answer these questions. Use Model 1 and predict the full IQ score of a female with size weight height a c b d As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if: a. the sample size n is greater than 30. b. the population proportion p is close to c. the underlying population is normal. d. np and n(1 p) are both greater than or equal to An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals: a. 15 b. 15/100 c. 15/ A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean is larger than 70 equals a. P(Z > 70) b. P(Z > 2) c. P(Z > 0.17) d. P(Z > 1.05) 33. In a multiple regression analysis, if the model provides a poor fit, this indicates that: a. the sum of squares for error will be large. b. the standard error of estimate will be large. c. the coefficient of determination will be close to zero. d. All of these choices are true. 5

6 Name: 34. In a multiple regression model, the standard deviation of the error variable ε is assumed to be: a. constant. b. 0. c

7 E205 Final: Version B Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: B PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION ANS: B PTS: ANS: D PTS: ANS: B PTS: ANS: D PTS: ANS: B PTS: ANS: D PTS: ANS: B PTS: ANS: D PTS: 1 REF: SECTION ANS: C PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: D PTS: 1 REF: SECTION ANS: A PTS: 1 REF: SECTION

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