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

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 = (x-\mu)/((\sigma)/(√(n)))`

`z = (2.6-2.8)/((0.88)/(√(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