Exercisemd.doc

Exercise 27 According to the local union president, the mean income of plumbers in the Salt Lake City area follows the normal probability distribution with a mean of $45,000 and a standard deviation of $3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? Required: (a) State the null hypothesis and the alternate hypothesis. (Omit the $ sign in your response.) H0: μ = $ H1: μ ≠ $ (b) State the decision rule for .10 significance level. (Round your answers to 2 decimal places.) Reject H0 if z or z (c) Compute the value of the test statistic. (Round your answer to 2 decimal places.) z value is (d) At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? H0. We that the mean salary is not $45,000. (e) Determine the p-value. (Round your answer to 4 decimal places.) The p-value is . The estimate of the population proportion is to be within plus or minus 0.05, with a 90 percent level of confidence. The best estimate of the population proportion is 0.21. How large a sample is required? (Round your answer to the nearest whole number.) Exercise 45 Nikes annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year. Requirement 1: What is the standard error of the mean in this experiment? (Round your answer to 2 decimal places.) Probability Requirement 2: What is the probability that the sample mean is between 6 and 7 pairs of sports shoes? (Round your z values to 2 decimal places and final answer to 4 decimal places.) Probability Requirement 3: What is the probability that the difference between the sample mean and the population mean is less than 0.25 pairs?