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one-sample inf EST

# one-sample inf EST - Practice Problems for One-sample...

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Practice Problems for One-sample Inference — Estimation © 2010 Radha Bose FSU Department of Statistics 1 1. What would be the z* critical value for 88% confidence? (You will have to find this one from scratch. Look at the picture on p.3 of the class notes to get an idea of how to find z*.) 2. A sample of 17 supermarkets charged a mean of \$6.49 for 1-lb packs of their store-brand ham. Let us assume that all such costs have standard deviation \$1.45. (a) Construct an appropriate 90% confidence interval for the mean cost of 1-lb packs of store-brand ham for all supermarkets, detail all the steps. (b) Interpret your margin of error in context. (c) Consumer Lookout speculates that the mean is around \$6.95. Based on the interval you calculated, is this a plausible figure? (d) If we wanted to keep the 90% confidence level but have a smaller margin of error, should we survey less or more supermarkets? (e) How many supermarkets would we need to survey if we wanted to be 99% confident that our cost estimate was within a quarter of the true population mean? 3. A survey showed that forty-five community college instructors had a mean annual salary of \$39,516, with standard deviation \$4027. (a) Construct an appropriate 95% confidence interval for the mean annual salary of all community college instructors, detail all the steps. (b) Some faculty members believe that the mean annual salary of all community college instructors is \$42,000. Based on the interval you calculated, is this a plausible figure? (c) Interpret the margin of error in context. (d) If we want to increase the confidence level without increasing the margin of error, how should we alter the survey? (e) If we wished to be 98% confident that our estimate was within \$500 of the true mean, how many community college instructors should we survey?

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Practice Problems for One-sample Inference — Estimation © 2010 Radha Bose FSU Department of Statistics 2 4. Fourteen students earned a mean grade of 85.7% on a test. The standard deviation of the fourteen grades was 10%.
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