The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean

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The Drying Time Of A Certain Type Of Paint Under Specified Test Conditions Is Known To Be Normally Distributed With Mean 1 (149.02 KiB) Viewed 13 times

The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 75 min and standard deviation 9 min. Chemists have proposed a new additive designed to decrease average drying time. It is believed that drying times with this additive will remain normally distributed with o = 9. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average drying time before such a conclusion is adopted. Let u denote the true average drying time when the additive is used. The appropriate hypotheses are Ho: μ = 75 versus Ha: μ< 75. Consider the alternative value μ = 74, which in the context of the problem would presumably not be a practically significant departure from Ho. (a) For a level 0.01 test, compute ß at this alternative for sample sizes n = 144, 1024, and 2,500. (Round your answers to four decimal places.) n 144 1024 2,500 0.1093 Z 0.0006 (b) If the observed value of X is X = 74, what can you say about the resulting P-value when n = 2,500? Is the data statistically significant at any of the standard values of a? (Round your z to two decimal places. Round your P-value to four decimal places.) 0.0849 B P-value 0 X