32 n-nu'm 33 Qnu'm 34- D-nu'm 35 nnu'm The middle interval around the population proportion which captures 95% of sample proportions of vehicles that exceed the speed limit is: 0 .81 8 0.882 What was the sample size to build this interval 4? 9 5 04 5 3 1 5 5 9 Among adult residents of a certain state ?0% more than 12 years of schooling. We want to build a middle interval [fab pg]: centered at 11: = 0.70 such that it captures 98% of all sample proportions within 10.025 [2 .5 percentage points] from the population proportion, what is the required sample size? 1 853 1 81 9 1 7' 5 7 1 69 8 Rick O'Shea is one of the two candidates running for the governor of a Midwestern state. Suppose Rick O'Shea has 4? percent of the votes among all the voters in the state. Just before the election a local TV news polls a random sample of 520 voters. What is the probability that the poll will predict Rick O'Shea winning the election? 0 .0 69 0 0 .0 3' 6? 0 .0 B5 2 0 .0 94-? What should the sample size be in order to reduce the probability of wrongly predicting Rick O'Shea's victory to 0.025? 1 0 64 9 94- 9 2 9 B68 Questions 19-22 are related to the following Beer bottles are filled so that they contain an average of 330 ml ofbeer in each bottle. Suppose that the amount ofbeer in a bottle is normally distributed with a standard deviation of 3.2 ml. 19 Mat is the probability that a randomly selected bottle will have less than 328 ml ofbeer? a 0.2660 b 0.2509 c 0.236? [1 0.2233 20 What middle interval captures the fill of 95% of all bottles? 325.5 334.5 324.7 335.3 323.? 336.3 322.6 33?.4 ..l'i5"-I 21 What is the probability that a randomly selected 6pack ofbeer will have a mean amount in 6 bottles less than 328 ml? 0.0403 0.0503 0.0629 0.0786 nnn'm 22 What middle interval captures the mean fill of 95% of all 6packs? a 325.6 334.4 b 326.3 333.7 c 326.9 333.1 {1 32?.4 332.6 Questions 23 and 24 are related to the following A recent article in a business journal reported that the mean annual salary for graduates from 30 top MBA programs 10 years after graduation is u = $274,500. Assume the standard deviation is o = $52,400. 23 What is the middle interval that captures 95% ofthe mean salaries from samples of size n = 60 graduates. a $258,589 $290,411 b $261,241 $287,759 c $263,451 $285,549 {1 $265,293 $28330? 24 Buns-Wu Keep the error probability at or. = 0.05. We want to build an interval which captures 95% ofthe sample means within $5,000 from the population mean. What is the minimum sample size that would yield such an interval? 422 384 349 317 Questions 25 and 26 are related to the following Consider the mean cost ofgetting a fouryear college degree. The middle interval which captures 95% of mean costs from samples of n = 60 graduates is 25 a b c d 26 Dunn-'51.: [EL i2} = $61,200 $66,200 What is the population mean cost ofgetting a college degree? $62,432 $63,063 $63,700 $64,343 In the previous question, suppose we want to build a middle interval which captures 95% of the sample means within $1,500 from the population mean. What is the minimum sample size that 180 167' 155 144 \f27 Dunu'm 28 nna'm If we take repeated samples of size n = 8 from this population of the students, the expected value of sample proportions would be . 0 .85 7 0 .81 6 0 .7 7 7 0 .740 If we take repeated samples of size n = 8 from this population of the students, the variance of sample proportions would be . 0.0259 0.0199 0.0153 0.0118 Question 29-31 are related to the following On a freei-ira},r 88% of vehicles violate the speed limit [11 = 0.88]. From the population of all vehicles on the freeway, you clock repeated random samples of size n = 500 vehicles. 29 a b c d 30 Dunn'm 31 Linda: What fraction of sample proportions [13's] from samples of size 600 fall within 10.03 [3 percentage points) from the population proportion? 0.980 2 0.9 61 0 0.942 2 0.92 3 7 The middle interval that captures 95% of sample proportions is, 0.875 0.885 0.871 0.889 0.864 0.896 0.852 0.908 To build a middle interval around the population proportion TI: such that 95% of all sample proportions deviate from the population proportion by no more than 10.02 [2 percentage points], what is the minimum sample size to yield this interval? 9 1 6 9 64 10 1 5 10 68