Download Midterm Solutions: Statistical Inference and Hypothesis Testing - Prof. Hal Sadofsky and more Exams Probability and Statistics in PDF only on Docsity! Practice midterm 2 Solutions: 1. (Multiple choice: 45 points total.) Circle the letter of the correct answer. 1A. We wish to study the average amount spent on salary by all non-profit corpo- rations in the United States. We choose 100 corporations at random to study. Our population is a. The 100 corporations we’ve chosen at random. b. The employees of non-profit corporations in the United States. c. The non-profit corporations in the United States. d. The salaries paid by our 100 corporations chosen at random. 1B. With respect to the same study, the average of the amounts paid in salary by the 100 corporations we’ve chosen at random is. a. A parameter. b. A statistic. c. The standard error. d. A variable. 1C. You design a special die. It has six sides as usual, but the probability of getting a number is distributed as follows: 1 2 3 4 5 6 Probability 0.2 0.3 0.1 0.1 ? 0.2 The probability of rolling a 5 is .1 , and the probability of rolling less than 4 is .6 . (a) 0.9 (b) 0.4 (c) 0.1 (d) 0.5 (e) 0.6. 1D. Which of the following is true? a. A practically important result must be statistically significant. b. A statistically significant effect must be practically important. c. When you use statistical inference you behave as if your sample is a random sample. d. Lack of significance shows H0 is true. 1E. Consider the following statements about estimating population means with z-tests. I. Other things being equal, the error decreases as the confidence level C decreases. II. Other things being equal, the error increases as the sample size increases. III. Other things being equal the error decreases if the standard deviation decreases. a. I and II. b. I and III, c. II and III. d. I, II and III. 1F. Which of the following would be strong evidence against the null hypothesis in a significance test? 1 (a) a very large P-value (b) a large sample size (c) a small sample size (d) a very small P-value The next several problems refer to this example: You are told that the average age of cars in use in the US, based on a survey over an 8 month period, is 9 years. You believe that the average age of cars in use in Eugene is greater than that. You ask the DMV for the ages of a random sample of 100 cars in Eugene, and do a t-test with the result. Let x̄ be the mean age of the 100-car sample. 1G. You are testing the value of a parameter µ. µ is: (a) the mean age of cars in use in the US. (b) the mean age of cars in use in Eugene. (c) the mean age of cars in the sample. (d) the probability that the mean age of cars in use is greater than 9. (e) the probability that the mean age of cars in use is equal to 9. 1H. The P -value is: (a) the probability that µ is at least x̄. (b) the probability of getting a random sample of 100 cars with mean ≥ x̄ if the mean age of cars in Eugene is 9. (c) the probability that this particular random sample has mean age x̄. (d) the probability that the null hypothesis is true. (e) the probability that the null hypothesis is false. 1I. The null and alternative hypotheses should be: (a) H0 : µ = 100, Ha : µ > 100 (b) H0 : µ = 9, Ha : µ > 9 (c) H0 : µ = 8, Ha : µ > 8 (d) H0 : µ = 100, Ha : µ < 100 (e) H0 : µ = 9, Ha : µ < 9 (f) H0 : µ = 8, Ha : µ < 8 (g) H0 : µ = 100, Ha : µ 6= 100 (h) H0 : µ = 9, Ha : µ 6= 9 (i) H0 : µ = 8, Ha : µ 6= 8 2. (5 points) (1) If a variable is distributed N(µ, σ), what distribution do means of samples of size n have?
