A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 767 hours. A random sample of 22 light bulbs has a mean life of 746 hours. Assume the population is normally distributed and the population standard deviation is 57 hours. At ?=0.08?, do you have enough evidence to reject the? manufacturer's claim? Complete parts? (a) through? (e).

(a) Identify the null hypothesis and alternative hypothesis. O A. Ho: 1 $746 O B. Ho: H = 746 O C. Ho: 12 767 (claim) Ha: H > 746 (claim) Ha: p # 746 (claim) Ha: H 767 OF. Ho: H # 767(claim) Ha: 1 2 746 Ha: $767 (claim) Ha: H = 767(b) Identify the critical value(s). Use technology. Zo = (Use a comma to separate answers as needed. Round to two decimal places as needed.)Identify the rejedion region(s)_ Choose the correct answer below. 0 A. O B. O c. Fail 10 reject Ho. Q Fail 10 reject Ho. Q Fail 10 reject Ho. Q Q Q Reject Ho. Reject Ho. , :4 Z Z (c) Identify the standardized test statistic. Use technology. 7= Round to two decimal places as needed.)(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. O A. Fail to reject Ho. There is sufficient evidence O B. Reject Ho. There is not sufficient evidence to reject the claim that mean bulb life is at to reject the claim that mean bulb life is at least 767 hours. least 767 hours. O C. Reject Ho. There is sufficient evidence to O D. Fail to reject Ho. There is not sufficient reject the claim that mean bulb life is at least evidence to reject the claim that mean bulb 767 hours. life is at least 767 hours