Consider a paint-drying situation in which drying time for a test specimen is normally distributed with $\sigma$ = 8. The hypotheses $H_0: \mu = 73$ and $H_a: \mu < 73$ are to be tested using a random sample of $n = 25$ observations. (a) How many standard deviations (of $\bar{x}$) below the null value is $\bar{x} = 72.3$? (Round your answer to two decimal places.) -0.44 standard deviations
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Step 1: The number of standard deviations below the null value is given by: $$ \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} $$ Show more…
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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 6. The hypotheses H0: μ = 75 and Ha: μ < 75 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of x̄) below the null value is x̄ = 72.3? (Round your answer to two decimal places.) (b) If x̄ = 72.3, what is the conclusion using α = 0.006? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) State the conclusion in the problem context. (c) For the test procedure with α = 0.006, what is β(70)? (Round your answer to four decimal places.) (d) If the test procedure with α = 0.006 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.) (e) If a level 0.01 test is used with n = 100, what is the probability of a type II error when μ = 76? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
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