Question

You can use both the t statistic and the z statistic to test hypotheses about the mean of population. The test that uses the t statistic is typically referred to as a t test, while the test that uses z statistic is commonly called a z test. Which of the following statements are true of the t statistic? Check all that apply. The t statistic uses the same formula as the z statistic except that the t statistic uses the estimated standard error in the denominator. The t statistic provides an excellent estimate of z, particularly with small sample sizes. The formula for the t statistic is t = (M – μ) / σM. The t statistic does not require any knowledge of the population standard deviation.

Answer 1

Answer:

Detailed elaborated answer is given below:

Answer 2

Using the concepts of the t-statistic and the z-statistic, it is found that the correct option is:

The t-statistic does not require any knowledge of the population standard deviation.

The z-statistic is given by:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which:

• X is the sample mean.
• $\mu$ is the population mean.
• $\sigma$ is the population standard deviation.
• n is the sample size.

• The standard error is $S_e = \frac{\sigma}{\sqrt{n}}$.

The t-statistic is similar to the z-statistic, the difference is that the sample standard deviation is used, not the population. Thus:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which:

• X is the sample mean.
• $\mu$ is the population mean.
• $s$ is the sample standard deviation.
• n is the sample size.
• The standard error is $S_e = \frac{s}{\sqrt{n}}$.

For large sample sizes, the sample and population standard deviations are close, thus t is a good estimate of z.

Thus, the correct option is:

The t-statistic does not require any knowledge of the population standard deviation.

A similar problem is given at https://brainly.com/question/16194574