Given: H_0: mu = 50 H_a: mu > 50 and alpha = 0.05 and a random sample of size 10

Question

Given: H_0: mu = 50 H_a: mu > 50 and alpha = 0.05 and a random sample of size 10 taken from a population that is N(mu, 250). (a) Like you did in the former question, indicate what is the distribution of X. (b) What is the critical value c? For the questions below, it will be useful to draw a table like we did in class: (c) What is the probability of rejecting the null when the null is true? (d) What is the probability of not rejecting the null when the null is true? (e) What is the probability of rejecting the null when mu = 60, i.e., when the null false?

Explanation / Answer

(a) From teh central limit theorem the mean of the samples will follow Normal Distribution

(b) Critical Value is 2.53 using standard deviation as square root of 250 which is variance = 15.8114

(c) p value is 0.005

(d) Not rejecting the null is 0.994294

(e) probability of rejecting the null when mean =60 is 0.000783 . Use normdist function in excel and specify x=10, mean=60, standard deviation as 15.8

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