A light bulb manufacturer guarantees that the mean life of a certain type of lig

Question

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 25 light bulbs has a mean life of 745 hours. Assume the population is normally distributed and the population standard deviation is 60 hours. At a = .02, do you have enough evidence to reject the manufacturer's claim? Complete problem showing all steps (null and alternate hypotheses, significance level (alpha). Write a complete decision rule. Use your TI, copy down the TI input screen and TI output screen. Write a complete conclusion.

Explanation / Answer

We need to test the null H0 : µ = 750 against the one-sided alternative H1 : µ < 745,

at level = 0.02. Since n is small, we will do a small-sample t-test.

The rejection region is t > t = 1.318, using the t table.

t = (X µ0) /(S/ n) = (745-750)/(60/ 5) = 0.416

Since t = 0.416 < 1.318,

H0 is accepted. Thus, there is significant evidence at 2% signifi- cance level that the mean number of life ia atleast 750.

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