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AP Statistics Review: Sampling Dist. & Confidence Intervals Name______________________ Part I. The facts you need to know. 1. Know the properties of a Sampling Distribution of Sample Mean. 2. Know the properties of a Sampling Distribution of Sample Proportions 3. Know each variable & whether it's a statistic or a population. 4. What is the Central Limit Theorem? 5. What is an unbiased statistic? 6. How does sample size, confidence level, proportion, & standard deviation affect a confidence interval? 7. Know the properties of the t-distribution. 8. Be able to construct a sampling distribution of means and find x and x. Part II. Computational Problems. 9. The nicotine content in a single cigarette of a particular brand has a distribution with a mean 0.8 mg and standard deviation 0.1 mg. If 100 of these cigarettes are analyzed, what is the probability that the resulting sample mean nicotine content will be a. less than 0.79? b. between 0.785 to 0.81? 10. The mean time for taxi and takeoff for commercial jets is 8.5 minutes and standard deviation is 2.5 minutes. Assume it is approximately normal. What is the probability that for 36 jets on a given runway the mean taxi and takeoff time will be at least 9 minutes? 11. It was found that about 73% of American men would favor a law requiring a police permit to buy a gun. What is the probability that in a sample of 38 American men, at least 66% will support gun permits? 12. A physician at the clinic in Grand Canyon Village estimates that 31% of the boating accidents on the Colorado River in the Grand Canyon National Park occur at Crystal Rapids. Suppose there are 28 recently reported boating accidents in the park, what is the probability that between 25% and 50% are from Crystal Rapids? 13. Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep the shipping channel is the sample proportion is greater than 0.25. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.20? 14. Retailers report that the use of cents-off coupons is increasing. It is reported the proportion of all households that use coupons is 0.77. Suppose that this estimate was based on a sample of 800 households. Construct a 95% confidence interval for the true proportion of all households that use coupons. 15. A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and must be discarded. A large shipment of plastic handles is received. The proportion of defective handles is of interest. How many handles from the shipment should be inspected to estimate p to within 0.1 with 95% confidence? 16. The Gallup Organization conducted a telephone survey on attitudes toward AIDS. A total of 1014 individuals were asked whether they agreed with the following statement: "Landlords should have the right to evict a tenant from an apartment because that person has AIDS." One hundred one individuals in the sample agreed with this statement. Use these data to construct a 90% confidence interval for the proportion who are in agreement with this statement. Give an interpretation of your interval. 17. The center for Urban Transportation Research released a report stating that the average commuting distance in the U. S. is 10.9 miles. Suppose that this average is actually the mean of a random sample of 300 commuters and that the sample standard deviation is 6.2 miles. Estimate the true mean commuting distance using a 99% confidence interval. 18. A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested to estimate with 95% confidence to within 0.1 lb, the average force required to break the binding? Assume that is known to be 0.8 lb. 19. Construct a 95% confidence interval for the population mean. You took a random sample of 12 twoslice toasters and found the mean price was $61.12 and the standard deviation was $24.62. 20. Construct a 90% confidence interval for the ACT scores shown below. 26 17 22 26 23 23 12 24 19 20 25 14 21. Explain what a 90% confidence level means. 23 21 21 23 25 20 10 22