Question: [10 points] Automotive LED bulbs are quite expensive, hence their lifetime is of importance to customers. A manufacturer of automotive LED bulbs claims that a new model will last more than 11000 hours. A testing agency wants to confirm this claim and selects a simple random sample of 60 LED bulbs of the new model for testing. The bulbs produce a sample average lifetime of 11200 hours, and a sample standard deviation of 800 hours. Construct a null and alternate hypothesis that the testing agency should use to confirm the manufacturer’s claim. Based on the sample data, what can the agency conclude? Use a 5% level of significance. Would your answer change if you used a 1% level of significance? Justify.

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