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 2.7 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 (-0.89) is not in the rejection region defined by the critical value (-2.33)

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.05)

Claim is null, reject the null and support claim as test statistic (-0.89) 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 (-0.89) is not in the rejection region defined by the critical value (-2.33)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.8
Alternative Hypothesis, Ha: μ < 2.8

Rejection Region
This is left tailed test, for α = 0.02
Critical value of z is -2.05
Hence reject H0 if z < -2.05

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (2.7 - 2.8)/(0.88/sqrt(61))
z = -0.89

Claim is alternative, fail to reject the null and cannot support claim as test statistic (-0.89) is not in the rejection region defined by the critical value (-2.05)

answered by: anonymous