Light bulbs of a certain type are advertised as having an average life-time of 8

Question

Light bulbs of a certain type are advertised as having an average life-time of 800 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random of 50 bulbs was selected. the lifetime of each bulb determined, and the following information obtained: average lifetime equal 738.44 hours and standard deviation of lifetimes equal to 38.2 hours. Should the customer purchase the light bulbs? Make the decision on a significance level of. 05? Make the decision on a significance level of. 01?

Explanation / Answer

a. H0 : mean = 800 hours

H1: mean <800 hours

z0 = -(800-738.44)/38.2 = -1.611

z0.95 = 1.645

So, z0 > - z0.95 so we cannot reject the null hypothesis

So, statistically mean is not less than 800 hours

b. z0.99 = 2.33

So, we again cannot reject the null hypothesis

So, statistically mean is not less than 800 hours

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