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 = 0.02, do you have enough evidence to reject the manufacturer's claim? Explain.  

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

This is a t-test with degrees of freedom = 25-1 = 24

Ho: mean = 750
Ha: mean does not equal 750

critical value is alpha = 0.02

Test statistic formula: t = (x-bar - )/(s/SQRT(n))
t-statistic = (745-750) / (60/ sqrt 25) = -0.416

Now, look up this t-value to find P(t<-0.416) = 0.3228

p-value = 0.322

T has an approximate standard normal distribution and for a=0.02 critical value
and since T> critical value do not reject H0, and conclude that there is insufficient
evidence for the manufacturer's claim

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