An electrical firm manufactures light bulbs that have a lifetime that is approxi

Question

An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a mean of 800 hours and a standard deviation of 40 hours. Test the hypothesis that = 800 hours against the alternative, 800 hours, if a random sample of 30 bulbs has an average life of 788 hours using the specific method described below. Use a 95% confidence level for your answer.

a. Compute and use a confidence interval to test the hypothesis.

b. Compute and use the calculated vs. critical method (i.e., the second method) to test the hypothesis.

c. Compute and use the p-value to test the hypothesis.

https://drive.google.com/file/d/0B-TpYwbWgGmUZGJjaEtOcXZZNU0/view?usp=sharing

Explanation / Answer

a)
mean = 800 , x = 788 , n = 30 , s =40

t = ( x - mean) /( s /sqrt(n))
= ( 788 - 800) /( 40 / sqrt(30))
= -1.643

b)
With alpha = .05, the critical values of z are -1.96 and +1.96. We reject if z < -1.96 or z > +1.96.

c) p value is calculated using t = -1.643 , df = 29
p value = .111183.
we fail to reject thenull hypothesis

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