Unformatted text preview: Exam 2 Spring 10 Review What can I bring to the exam? You may have one 8 ½ by 11 sheet of paper with whatever handwritten notes you wish to put on it front and back. You may have “clean” scratch paper for doing computations. You may have a calculator. You may have a table of the normal distribution. Use blank spaces on the exam paper or scratch paper to do your computations. Your proctor will return the exam and any scratch paper you use to the Division of Continuing Education. How long do I have to take the exam? The exam is 50 minutes. Practice Exam Questions Lesson 09: Probability. What are the basic properties of probability? What are the two methods of determining probabilities discussed in the slides? 1. 4 pts. A survey of owners of cars showed the following probabilities for the various colors. Color of car Probability black silver blue red other
.30 .25 .20 .10 ?? What is the probability that the color of the car is “other”? prob = ________ 2. 4 pts. The probability of being struck by lightning is 1/700,000. This is an example of a. Determining probability by equally likely outcomes b. Determining probability using data c. Determining probability from mathematical equations Lesson 10: Sampling. What is a population and what is a sample? In what sense is a random sample a representative sample? What does the soup tasting analogy tell us about sample sizes for opinion polls? What are some of the things that can go wrong with sampling? 1 3. 4 pts. The U.S. Census Bureau sends a “short form” to every household in the United States every 10 years to gather basic information. In addition, they send a “long form” to a sample of about 17% of the households asking for more detailed information. What is the population that is sampled by the U.S. Census Bureau? a. All households in the U.S. b. All households in the U.S. that respond to the short form. c. The 17% of households that receive the long form. 4. 4 pts. California has about 13 times more registered voters than does Kansas. Suppose pollsters wish to take polls of registered voters in both states to predict the next election. True or false: In order for the polls to have the same accuracy, the sample size of the poll in California should be about 13 times larger than the sample size of the poll in Kansas. a. True b. False Lesson 11: Margin of error for proportions. Know the difference between a proportion and a percent. Understand the key question that we ask about population and sample proportions. What are the shape of the distribution, the mean, and standard deviation of sample proportions? What is the formula for the margin of error of sample proportions? Note: there are formulas here that would be useful to include on your 8.5 by 11 sheet of paper that you may bring to the exam. 5. 4 pts. The numbers of men and women in a city of 100,000 residents are approximately equal. Suppose we take a random sample of 100 individuals from this city and compute the proportion of men (or women) in the sample? With 95% certainty, how close to 1/2 will the sample proportion be? 0.50(1 − 0.50)
50(100 − 50)
.50(1 − .50) b. ± 1.96 c. ± 1.96 a. ± 1.96
100
100
100,000 6. 6 pts. Among the 20,000 students at a certain university, 45% live off campus. Suppose we take random sample of 400 students. With 95% certainty, what percent of those in the sample will live off campus? (Choose the option closest to the correct value.) a. 40% to 50% b. 44% to 46% c. 42% to 48% 2 Lesson 12: Estimating population proportions. In lesson 11 we started with a population proportion and asked where the sample proportion would likely fall. In this lesson we start with the sample proportion and ask where the population proportion is likely to fall. The two key ideas are margin of error and confidence interval. 7. 6 pts. An inspector took a random sample of 100 shipments of “name brand” shoes and found that 15 shipments contained shoes that were not genuine. What is a 95% confidence interval for the percentage of shipments that contain shoes that are not genuine? (Choose the option closest to the correct values.) a. 14.93% to 15.07% b. 11% to 19% c. 8% to 22% 8. 6 pts. A poll of U.S. residents was taken to determine the mood of the country. One of the questions was, “Is your view of the economy more positive or more negative than it was last year?” The margin of error for the percentages of positive and negative responses to this and other such questions was reported to be 2.4 percentage points. What is the sample size of the poll? (Choose the option closest to the correct value.) a. 2400 b. 1800 c. 2.4 percent of the population 9. 6 pts. Suppose candidates Smith and Jones are running against each other for a seat in Congress. The day before the election, a random sample of 350 likely voters showed that 52% favored Smith. What is the best interpretation of this result? a. Smith will likely win the election b. The race is too close to call Lesson 13: Distribution of sample means. In Lessons 11 and 12 we deal with population and sample proportions. In Lessons 13 and 14, we deal with population and sample means. We ask, “How close is the sample mean likely to be to the population mean?” To answer this question we need to know the distribution and margin of error of sample means. As you work the exam, be sure you know whether a question is about means or whether it is about proportions (or percents). The ideas are similar but the formulas are different. 10. 6 pts. A population of incomes has a mean of μ = $35,000 and a standard deviation σ = $5000. Suppose the sample size is n = 100. What is the margin of error of the sample means? m.o.e. = ________ 3 11. 4 pts. Which of the following is not a property of the distribution of sample means? a. The mean of the sample means equals the population mean. b. The standard deviation of the sample means equals the population standard deviation. c. The distribution of sample means is bell‐shaped for large sample sizes. Lesson 14. Estimating a population mean. In this lesson we assume that we have taken a random sample from a population and we have computed the sample mean and sample standard deviation. We want to know the margin of error of the sample mean, and we want to make a confidence interval for the population mean. 12. 6 pts. A random sample of 30 two‐bedroom apartments listed for rent in the newspaper had an average rental price of $575 per month with a standard deviation$45. Which of the following is a 95% confidence interval for the mean rental price of the population of two‐bedroom apartments? (Select the option closest to the correct answer). a. $571 to $579 b. $567 to $583 c. $559 to $591 13. 4 pts. A data set of 100 numbers has a bell‐shaped distribution with a mean of 48 and a standard deviation of 12. Suppose these numbers were selected randomly from a population. Which of the following intervals would contain about 95% of the data values in the population? 12 a. 48 ± 1.96
= 48 ± 2.4 b. 48 ± 1.96(12) = 48 ± 24 100 14. 6 pts. A car manufacture claims its cars get an average of 28.0 miles per gallon. A consumer’s group thought this was too high. They took a random sample of 36 such cars and got an average of 27.3 miles per gallon with a standard deviation of 3.0 miles per gallon. Which of the following is the better interpretation of this result? a. The claimed value of 28.0 mpg is within the margin of error of the sample mean. The concern of the consumer group is not confirmed by the data. b. The claimed value of 28.0 is likely a bit too high given that the sample mean is 27.3. 4 ...
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 Fall '08
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