# You believe the mean annual kilowatt usage of U

You believe the mean annual kilowatt usage of U.S. residential customers is less than 10,800. You do some research and find that a random sample of 30 residential customers has a mean kilowatt usage of 10.700, with a standard deviation of 280. You conduct a statistical experiment where_{}and_{}. At_{}, explain why you cannot reject_{}.

**Solution: **We need to test

_{}

This corresponds to a left-tailed t-test. The t-statistics is computed as:

_{}

The p-value for the test (for 29 degrees of freedom) is given by:

_{}

Since the p-value is greater than 0.01, *we fail to reject the null hypothesis.*

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