Answer to Question #211871 in Statistics and Probability for Anna

Question

A manufacturer of a lightbulb claimed that its lightbulbs have a mean lifetime of 700 hours with a standard deviation of 120 hours. You purchased 144 of these lightbulbs with the idea that you would purchase more if the mean lifetime of your sample were more than 680 hours. What is the probability that you will not buy again from this manufacturer?

Answer 1

One sample z-test.

$H_0: \mu=700.$

$H_a: \mu<700.$

Test statistic: $z=\frac{680-700}{\frac{120}{\sqrt{144}}}=-2.$

P-value: $p=P(Z<-2)=0.0228.$

The probability that I will not buy again from this manufacturer is 0.0228.