What does the null hypothesis typically specify about the population mean?

What does the null hypothesis typically specify about the population mean?

• A. The mean is greater than a specified value
• B. The mean is less than a specified value
• C. The mean is equal to a specified value
• D. The mean is not equal to a specified value

Answer: (C)

The null hypothesis starts with a precise, testable claim about the population mean. In most mean tests, that claim is that the population mean equals a specific value. This equality is what makes the hypothesis test workable: you can use the sampling distribution of the sample mean under the assumption that the true mean is that value to see how likely your observed data would be. If the data look very unlikely under that equality, you might reject the null in favor of an alternative. The other statements—mean greater than, less than, or not equal to the value—represent possible alternative hypotheses, not the null. So the statement that the population mean equals the specified value is the one that best describes the null.

The null hypothesis starts with a precise, testable claim about the population mean. In most mean tests, that claim is that the population mean equals a specific value. This equality is what makes the hypothesis test workable: you can use the sampling distribution of the sample mean under the assumption that the true mean is that value to see how likely your observed data would be. If the data look very unlikely under that equality, you might reject the null in favor of an alternative. The other statements—mean greater than, less than, or not equal to the value—represent possible alternative hypotheses, not the null. So the statement that the population mean equals the specified value is the one that best describes the null.