A light bulb manufacturer guarantees that the mean life of a

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 775 hours. A random sample of 68 light bulbs has a mean life of 769 hours with a standard deviation of 90 hours. Do you have enough evidence to reject the manufacturer\'s claim Use o -0.03. G) Identify the null hypothesis and alternative hypothesis OA. Hot 769 OB. Ho: 769 OC. o: 775 Ha u 769 Hai uz 769 H S775 OE. 0: 775 OF. 0: 775 OD. 0: S769 Ha: 769 775 H,: 775 (b) Identify the critical value(s). (Use a comma to separate answers as needed. Round to two decimal places as needed.) c Identify the standardized test statistic z Round to two decimal places as needed.) d) Decide whether to reject or fail to reject the null hypothesis OA. Fail to reject Ho. There is not sufficient evidence to reject the claim OB. Reject Ho-There is sufficient evidence to reject the claim that that mean bulb life is at least 775 hours. mean bulb life is at least 775 hours. Oc. Reject Ho. There is not sufficient evidence to reject the claim that OD. Fail to reject Ho. There is sufficient evidence to reject the claim mean bulb life is at least 775 hours. that mean bulb life is at least 775 hours.

Solution

(a) E

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(b) It is a left-tailed test.

Given a=0.03, the critical value is Z(0.03)=-1.88 (from standard normal table)

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(c) The test statisitc is

Z=(xbar-mu)/(s/vn)

=(769-775)/(90/sqrt(68))

=-0.55

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(d)A