Question

Which of the following statements is true regarding the T Test for a mean:

a. The t test for a mean is a statistical test for a population mean. The t-test can be used when the population is normal, the population standard deviation is unknown and the sample size is less than 30
b. The t test for a mean is a statistical test for a population mean. The t-test can be used when the population is normal, the population standard deviation is known and the sample size is at least 30
c. The t test a statistical test for the variance or standard deviation. The t-test can be used when the population is normal, the population standard deviation is known and the sample size is at least 30
d. All of the above
e. None of the above

Answer 1

The correct statement is a; the T-Test for a mean is used when the population mean is being tested, the population standard deviation is unknown, and the sample size is less than 30.

Step-by-step explanation:

The t-test can be used when the population is normal, the population standard deviation is unknown and the sample size is less than 30. This is because the T-test is designed to estimate the population mean when we do not know the population standard deviation. Instead, we use the sample standard deviation as an estimate. The Student's t-distribution is appropriate when the sample is a simple random sample from a population that is approximately normally distributed, or if the sample size is large (though not necessarily above 30, as was believed before the advent of graphing calculators and computers). Now, the Student's t-distribution is used whenever the sample standard deviation is used as an estimate for the unknown population standard deviation.