Let X denote the life length in hours of a battery Suppose X

Last updated: 12/14/2023

Let X denote the life length in hours of a battery Suppose X is known to be normally distributed with standard deviation o 2 25 hours A random sample of 12 batteries has an average life of x 51 3 hours We are interested in determining whether there is evidence to support the claim that mean battery life exceeds 50 hours Using a level of significance of 0 05 answer the following questions Part a 4 points State the null and alternative hypothesis for the appropriate hypothesis test Part b 5 points Identify the test statistic and p value Part c 3 points State the conclusion of the test in the problem context Part d 5 points What is the Type II error probability for the test if the true mean life is 51 0 hours Part e 3 points If the true mean life is 51 0 hours what is the power of the test Part f 5 points What value of n is required to satisfy a 0 05 and 0 01