1 Fall 2012 STAT 110 Exam 3 Practice AA+B θθ+1 a1p1 + a2p2 + … + akpk2 1) A random outcome is unpredictable in the short run, but has a regular, predictable pattern in the long run. a. TRUE b. FALSE 2) If you toss a coin 10,000 times to determine if it is fair, what type of probability are you using? a. Empirical b. Theoretical c. Personal d. Random 3) Identify the legitimate assignment of probabilities for a sample space with 4 outcomes a. 1.1, 0.3, 0.3, 0.5 b. 0.1, 0.3, 0.7, 0 c. 0.2, 0.4, 0.6, -0.2 d. 0.2, 0.2, 0.2, 0.4 A psychologist gives subjects a set of puzzles and measures how many are completed in 5 minutes. From data from many subjects, the psychologist establishes the following probability model: Puzzles solved 1 2 3 4 5 Probability ? 0.50 0.20 0.10 0.10 4) What is the probability that a subject will complete only one puzzle? a. 0.05 b. 0.10 c. 0.15 d. 0.20 5) What is the complement of completing 3 or fewer puzzles? a. 3 or more puzzles b. more than 4 puzzles c. exactly 3 puzzles d. more than 3 puzzles 6) If you flip a fair coin 5 times and get 5 heads in a row, what is the probability that you will get a head on the 6th flip? a. Less than 0.50 b. More than 0.50 c. 0.50 d. Unknown A store hands out scratch-off tickets with cash prizes printed on them (probability model is table at right). 7) What is the expected winning for a customer? (a) =$52.5 (b) =$35 (c)00.95+50.04+1000.01=$1.20 (d) 0.95+0.04+0.01=$1.00 8) What is the probability that a customer entering the store will not win one of the cash awards? (a) 0.95 (b) 0.01 (c) 0.04 (d) 0.05 9) If several thousand customers average their winnings, we can expect their average winnings to be a. close to the median amount b. close to the expected value c. close to the probability of winning d. close to $15 Outcome $0 $5 $100 Probability 0.95 0.04 0.013 10) Two events are independent if a. They share outcomes in common (have an intersection) b. They share no outcomes in common (have no intersection) c. The occurrence of one event does not affect the occurrence of the other event d. They are in different sample spaces 11) TRUE or FALSE For a certain car, the events “car wins the race” and “car loses the race” would be considered disjoint a. TRUE b. FALSE 12) Suppose the odds for passing a class are 10 to 1. Find the probability of passing the class. a. 1/10 b. 1/11 c. 9/10 d. 10/11 13) Find the probability (using a fair six-sided die) of rolling a “1” on the first roll AND rolling a “1” on the second roll. a. 1/6 b. 1/6 + 1/6 = 2/6 =1/3 c. (1/6)(1/6) = 1/36 d. 1/6 + 1/6 – (1/6)(1/6) = 11/36 14) The Law of Large Numbers says that for a random sample, the sample mean will a. be normally distributed b. be normally distributed with a large enough sample size c. be equal to the population mean d. be equal to the population mean with a large enough sample size 15) What is true about the sampling distribution of the sample proportion? a. It is skewed b. Nothing is known about it c. It has a normal distribution as long as the sample size is large d. It is not a distribution e. It always has a normal distribution4 A survey is being conducted using a random sample of 120 economists, asking whether paying off debt is the best usage of federal stimulus funds by the state. Of those, 33 think it is the best usage of the funds. The true percentage of all economists thinking it is the best usage is 40%. 16) Find the sample proportion, p, of those that think paying off debt is the best use of funds. a. =27.5% b. 40% c. .. d. .. e. .. 17) Find the mean of the distribution of the (all possible) sample proportions for those that think paying off debt is the best use of funds. a. =27.5% b. 40% c. .. d. .. e. .. 18) Find the standard deviation of the distribution of (all possible) sample proportions for those that think paying off debt is the best use of funds. a. =27.5% b. 40% c. .. d. .. e. .. 19) The variability in the distribution for (all possible) p’s will ______________ if we consider a larger sample size a. get larger b. get smaller c. stay the same d. change, but we do not know how Wing lengths (inches) were measured from fledglings at an avian nesting site. A 90% confidence interval used to estimate the mean wing length is (2.163, 3.434). 20) Choose the correct interpretation. a. We are 90% confident that sample mean wing length in fledglings like these is at least 2.163 inches and at most than 3.434 inches. b. We are 90% sure that true mean wing length in fledglings like these is at least 2.163 inches and at most than 3.434 inches. c. We are 90% confident that true mean wing length in all fledglings like these is at least 2.163 inches and at most 3.434 inches. 21) Suppose another confidence interval is computed with 80% confidence instead of 90% confidence. The resulting 80% confidence interval will a. be the same width b. be wider c. be narrower d. not enough information to say what it will look like5 Researchers studied the effect of a houseplant fertilizer on radish sprout growth. They randomly selected some radish seeds to serve as controls, while others were planted in aluminum planters to which fertilizer sticks were added. Researchers were looking for evidence that the mean radish height is smaller when fertilized. 22) Find the HO, the null hypothesis. a. mean radish height is equal under fertilized or control conditions b. mean radish height is larger under fertilized condition c. mean radish height is smaller under fertilized condition d. mean radish height is different under fertilizer and control conditions 23) Find the HA, the alternative hypothesis. a. mean radish height is equal under fertilized or control