To test the null hypothesis that the average lifetime for a particular brand of

Question

To test the null hypothesis that the average lifetime for a particular brand of bulb is 750 hours vs. the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used. If the standard deviation is 50 hours and is equal to 0.01, what values for mean will result in rejection of the null hypothesis? (Show all work)

Explanation / Answer

Given =50, n=75 Ho:=750 Ha: not equal 750 =0.01, Z(0.005)=-2.58 (check normal table) When test statistic Z=(xbar -)/(/n) < -2.58or (xbar-)/(/n) > 2.58, we will reject nullhypothesis. So (xbar -)/(/n) < -2.58 --> (xbar -750)/(50/sqrt(75)) xbar < 750-2.58*(50/sqrt(75)) = 735.1 or (xbar -)/(/n) > 2.58 --> xbar > 750+2.58*(50/sqrt(75)) = 764.9

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