Question

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 712.8 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim using the test statistic? @See text pages 368-370

A. Claim is the null, fail to reject the null and support claim as test statistic (-0.83) is not in the rejection region defined by the critical value (-1.645)

B. Claim is the alternative, fail to reject the null and cannot support claim as the test statistic (-0.83) is in the rejection region defined by the critical value (-1.96)

C. Claim is the alternative, reject the null and support claim as test statistic (-0.83) is not in the rejection region defined by the critical value (-1.96)

D. Claim is the null, reject the null and cannot support claim as test statistic (-0.83) is in the rejection region defined by the critical value (-1.645)

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   720

H_a : < 720

Test statistic = z

= ( - ) / / n

= (712.8 - 720) / 62 / 51

= -0.83

= 0.05

Z _0.05 = -1.645

Critical value = -1.645

Test statistic < Critical value

Fail to reject the null hypothesis .

A. Claim is the null, fail to reject the null and support claim as test statistic (-0.83) is not in the rejection

region defined by the critical value (-1.645)