Expert: Vivian - 10/2/2008

Question
A lightbulb i supposed to have a expected life expectancy of a 1000 hours normally distributed with a variance of 100 hours.

I pick out ten bulbs and found the average life expectancy to be 995 hours.

Is the supposed life expectancy reasonable.

How do I approach this problem

xie xie ni

Answer
Here we want to test
the null hypothesis: a lightbulb has an expected life expectancy of 1000 hours vs. the alternative hypothesis: the expected life expectancy of a light bulb is not 1000 hours.

The sample mean of the life expenctancies of light bulbs is normal distributed with mean 1000 hours and variance 10 hours.

How do I calculate the variance? var(a*X)= a^2*var(X) where X is a random variable and ‘a’ is a constant. For details, please take a look at the first formula under the Properties section at
http://en.wikipedia.org/wiki/Variance

P-value of a statistical hypothesis test is the probability of getting a value of the test statistic as extreme as or more extreme than that observed by chance alone, if the null hypothesis is true.

p-value = probability for the sample mean to be larger than or equal to 995 hours under the normal distribution with mean 1000 and variance 10=1- NORMDIST(995,1000,SQRT(10),TRUE) =0.94 >> 0.05 where NORMDIST is a statistical function in excel.

Therefore the supposed life expectancy is reasonable.