Understanding Hypothesis Testing for Mean

What is the null hypothesis in a hypothesis test for the mean?

• The sample mean is equal to the population mean.

• The sample mean is not equal to the population mean.

• The population mean is greater than the sample mean.

• The population mean is less than the sample mean.

Which of the following is a common significance level used in hypothesis testing?

• 0.01

• 0.05

• 0.10

• All of the above

What is the test statistic used in a hypothesis test for the mean when the population standard deviation is known?

In hypothesis testing, what does a p-value represent?

• The probability of the null hypothesis being true.

• The probability of observing the sample data, or something more extreme, if the null hypothesis is true.

• The probability of the alternative hypothesis being true.

• The probability of making a Type I error.

What is a Type I error in hypothesis testing?

• Failing to reject the null hypothesis when it is false.

• Rejecting the null hypothesis when it is true.

• Failing to reject the alternative hypothesis when it is true.

• Rejecting the alternative hypothesis when it is false.

If the p-value is less than the significance level, what decision should be made regarding the null hypothesis?

• Fail to reject the null hypothesis.

• Reject the null hypothesis.

• Accept the null hypothesis.

• Accept the alternative hypothesis.

What is the alternative hypothesis in a two-tailed test for the mean?

• The population mean is equal to a specified value.

• The population mean is not equal to a specified value.

• The population mean is greater than a specified value.

• The population mean is less than a specified value.

• It is used when the population standard deviation is known.

• It is used when the population standard deviation is unknown and the sample size is small.

• It is always symmetric and has heavier tails than the normal distribution.

• Both B and C

What is the critical value in hypothesis testing?

• The value that separates the rejection region from the non-rejection region.

• The value of the test statistic.

• The value of the p-value.

• The value of the sample mean.