Question

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 6. The hypotheses H0: μ = 73 and Ha: μ < 73 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) (b) If x = 72.3, what is the conclusion using α = 0.01? (Round your answers to two decimal places.) test statistic z = -0.58 critical value z = 0.31 What can you conclude? Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. (c) What is α for the test procedure that rejects H0 when z ≤ −2.56? (Round your answer to four decimal places.) (d) For the test procedure of part (c), what is β(70)? (Round your answer to four decimal places.) (e) If the test procedure of part (c) is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)

Answer 1