Question

A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.6 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic?

Answer 1

Answer:

Claim : A computer manufacturer estimates that its cheapest screens will last less than 2.8 years.

$H_0:\mu\geq 2.8\\H_a:\mu < 2.8$

n = 61

Since n > 30

So , we will use z test

x = 2.6

$\sigma = 0.88$

Formula : $z = \frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{2.6-2.8}{\frac{0.88}{\sqrt{61}}}$

$z =-1.775$

Refer the z table

p =0.0384

α=0.02

p value > α

So, we accept the null hypothesis

So, the claim is false that A computer manufacturer estimates that its cheapest screens will last less than 2.8 years