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?

Claim is alternative, reject the null and support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)

Claim is null, fail to reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)

Claim is null, reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

So, the alternative hypothesis is the claim.

Since the population standard deviation is known, we use Z-test.

The test statistics value is given by:

Since this is a left-tailed test, the critical value is given by:

Since the test statistic value lies to the right of the critical value, so we do not have sufficient evidence to reject the null hypothesis H0. So, we fail to reject the null and cannot support the claim.

Hence 3rd option is the correct option.