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A review sheet for test 2 in econ 230, focusing on probability distributions, mean and standard deviation, sampling distributions, and confidence intervals. It includes reading materials from chapters 5, 6, 7, and 8, as well as important terms and phrases. The document also provides solutions to various problems.
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Readings the test will cover: Chapter 5: Sections 5.1-5.4, 5. Chapter 6: Sections 6.1-6. Chapter 7: Chapter 8: Sections 8.1-8. Important terms and phrases: Chapters 5 and 6:
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3. A package of frozen vegetables has a label that says “contents 32 oz.” However, the company that produces these packages knows that the weights are normally distributed with mean 32 oz. and standard deviation 2 oz. If a package is chosen at random, what is the probability that it will weigh a) more than 35 oz.? b) less than 30 oz.? c) between 30 and 35 oz.? 4. Suppose that the test scores for a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100. a) What percentage of those taking the exam score between 350 and 450? b) A student scoring above 400 is automatically admitted. What percent score above 400? c) The upper 5% receive scholarships. What score must a student make on the exam to receive a scholarship? 5. The heights of adult males are normally distributed with a mean height of 70 inches and a standard deviation of 2.6 inches. How high should the doorway be constructed so that 90% of the men can pass through it without having to bend? 6. The heights of college age men are known to be normally distributed with a mean of 68 in. and a standard deviation of 3 in. a) What is the probability that the mean height of a random sample of nine college men is between 67 and 69 inches? b) What is the probability that the mean height of a random sample of 100 college men is between 67 and 69 inches? c) Compare your answers to parts a and b. Was the probability in part b much higher? Why would you expect this? 7. According to Bride’s Magazine , the cost of a wedding these days can be expensive when the costs of the reception, engagement ring, bridal gown, and pictures-just to name a few- are included. Shao Wei wants to estimate the mean cost for a wedding. From a random sample of 115 recent U.S. weddings, the mean cost was $18,945 and the standard deviation was $8,280. Construct a 99% confidence interval for the population mean cost for a wedding. 8. In a survey of 2000 adults from the U.S. age 65 and over, 1320 received a flu shot. a) Find a point estimate for the population proportion p of adults receiving a flu shot. b) Construct a 90% confidence interval for the population proportion. 9. An economist wants to estimate the mean income for the first year of work for college graduates. Determine the minimum required sample size to construct a 95% confidence interval such that the confidence interval goes from $500 below the mean to $500 above the mean. Assume that the population standard deviation is $6250.