Answer to Question #346631 in Statistics and Probability for Zack

Question

A manufacturer of tires claim that their tire has a mean life of at least 50,000kms. A random sample of 28 of these tires is tested and the sample mean is 33,000kms. Assume that the population standard deviation is 3,000kms and the lives of the tires are approximately normally distributed.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu\ge50000$

$H_1:\mu<50000$

Given

$n=28<30,$ but we assume that the lives of the tires are approximately normally distributed.

$\sigma$ s known, $\sigma=3000.$

$\bar{x}=33000$

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.