409Pr2 - Practice Problems 1. The label on 1-gallon can of...

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Unformatted text preview: Practice Problems 1. The label on 1-gallon can of paint states that the amount of paint in the can is sufficient to paint at least 400 square feet (on average). Suppose the amount of coverage is approximately normally distributed, and the overall standard deviation of the amount of coverage is 25 square feet. A random sample of 16 cans yields the sample mean amount of coverage of 389 square feet. a) Test the claim on the label at a 5% level of significance. b) Find the P-value of the test in part (a). c) Using the P-value from part (b), state your decision (Accept H or Reject H ) for α = 0.03. d) Suppose the actual value of the mean coverage of all 1-gallon cans is 395 square feet. Then in part (a), _____ was made. ( Circle one ) Type I Error Type II Error Correct decision Cannot tell e) Suppose the actual value of the mean coverage of all 1-gallon cans is 395 square feet. Then in part (c), _____ was made. ( Circle one ) Type I Error Type II Error Correct decision Cannot tell f) Construct a 95% confidence interval for the true mean coverage of all 1-gallon cans. g) How large a sample should be taken to estimate the mean coverage of all 1-gallon cans to within 4 square feet with 95% confidence? h) Find the power of the test in part (a) if the actual value of the mean coverage of all 1-gallon cans is 395 square feet. i) Find the probability of Type II Error of the test in part (a) if the actual value of the mean coverage of all 1-gallon cans is 395 square feet. j) Find the power of the test in part (a) if the actual value of the mean coverage of all 1-gallon cans is 385 square feet. 2. A researcher wishes to determine whether the starting salaries of high-school math teachers in private schools are different from those of high-school math teachers in public schools. She selects a sample of new math teachers from each type of school and calculates the sample means and sample standard deviations of their salaries. Assume that the populations are normally distributed and the population variances are equal. Private Public sample size 10 7 sample mean $26,800 $26,300 sample standard deviation $600 $546 a) Perform the appropriate test at a 1% level of significance. b) Find the p-value of the test in part (a). c) Suppose instead we wish to test H : μ Private = μ Public vs. H 1 : μ Private > μ Public . What is the p-value for this test? 3. A large insurance company wants to determine whether the proportion of male policyholders who would not submit auto insurance claims of under $500 is higher than the proportion of female policyholders who do not submit claims of under $500. A random sample of 400 male policyholders produced 320 who had not submitted claims of under $500, whereas a random sample of 300 female policyholders produced 219 who had not submitted claims of under $500....
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This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.

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409Pr2 - Practice Problems 1. The label on 1-gallon can of...

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