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 701.6 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? claim is the alternative, reject the null and support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.96) Claim is the null, fail to reject the null and cannot support claim as test statistic (-2.12) is not in the rejection region defined by the critical value (-1.645) Claim is the alternative, fail to reject the null and cannot support claim as the test statistic (-2.12) is in the rejection region defined by the the critical value (-1.96) Claim is the null, reject the null and support claim as test statistic (-2.12) 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

= 701.6

= 720

= 62

n = 51

Test statistic = z

= ( - ) / / n

= (701.6 - 720) / 62 / 51

= -2.12

Test statistic = -2.12

= 0.05

Z = Z _0.05 = -1.645

Critical value = -1.645

Test statistic > Critical value

Reject the null and support claim as test statistic (-2.12) is in the rejection region defined by the critical value (-1.645) .