Your muffler factory claims to manufacture mufflers with a lifespan of more than 10000 miles of usage. A consumer group tests this claim at the 95 percent significance level, and finds that a sample of 64 mufflers have a mean lifespan of 10002 miles, with a standard deviation of 10 miles. Test the following alternative hypothesis using this data, and interpret the results:

Question

Your muffler factory claims to manufacture mufflers with a lifespan of more than 10000 miles of usage. A consumer group tests this claim at the 95 percent significance level, and finds that a sample of 64 mufflers have a mean lifespan of 10002 miles, with a standard deviation of 10 miles. Test the following alternative hypothesis using this data, and interpret the results:
(a) manufacturer's hypothesis : Ha : mean u is greater than 10000
(b) consumer group's hypothesis : Ha: mean u is less than 10000
(c) if the manufacturer wanted to state that the survey proved their claim to be true, what should mean x have been?
(d) if the consumer group wanted to state that the survey proved the manufacturer's claim to be false, what should mean x have been?