Question

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 753 hours. A random sample of 28 light bulbs has a mean life of 726 hours. Assume the population is normally distributed and the population standard deviation is 64 hours. At alphaequals0.05​, do you have enough evidence to reject the​ manufacturer's claim?

Answer 1

P (z for -2.23) is -0.9871

Explanation:

Given data

mean life x = 753 hours

sample n = 28

mean y = 726

standard deviation SD = 64 hours

to find out

check to have enough evidence to reject his claim

solution

we know that given mean is x ≥ 753

we found mean = 726

so difference = y - x = 726 - 753 = -27

and we know σ = SD/√n = 64 / √28 = 12.094896

Z = y - x / σ

Z = -27 / 12.09

Z = -2.23

so probability value

P (z for -2.23) is -0.9871

so z value is less than alpha = 0.05​

so reject

so this is enough evidence to reject his claim