About Vivian Expertise I can answer questions on probability, distributions, statistical inference, statistical estimation, hypothesis testing, analysis of categorical data, linear regression, generalized linear regression, ANOVA, and linear mixed models. I cannot answer questions on stochastic processes.
Experience I have worked as a research assistant at the University of Michigan, Ann Arbor for two years.
Organizations American Statistical Association
Education/Credentials University of Michigan, Ann Arbor
Master of Science
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
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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.
