Consider the following hypotheses H0 Mu leq 500 H1Mu 500 Gi

Consider the following hypotheses H0: Mu leq 500 H1:Mu > 500 Given that Sigma=34, n=36, Mu=502, and alpha=0.02,calculate Click here to view page 1 of the Standard Normal Distribution table. Click here to view page 2 of the Standard Normal Distribution table. The probability of committing a Type II error is . (Round to four decimal places as needed) Enter your answer in the answer box, then click Check Answer.

Solution

Ho: Mu <= 500

H1: Mu > 500

Sigma = 34

N = 36

Mu = 502

Alpha = .02

The probability of committing a type II error is _____

A type II error is failing to reject the null hypothesis when it is not true.

Looking up .98 (1-alpha) on a standard normal table, the critical z score is 2.05.

The null hypothesis will not be rejected if z is less than 2.05.

Convert this to an x value:

X = Z*sigma + mu

X = 2.05*34/sqrt 36 + 500

X = 511.617

So the null hypothesis will not be rejected when x is less than 511.617.

Next, find the probability of getting an x value of 511.617 or less when mu is 502:

Convert to a Z:

Z = (511.617