8.3 Distribution needed for hypothesis testing

Earlier in the course, we discussed sampling distributions. Particular distributions are associated with hypothesis testing. Perform tests of a population mean using a normal distribution or a student's-t distribution. (Remember, use a student's-t distribution when the population standard deviation is unknown and the distribution of the sample mean is approximately normal.) In this chapter we perform tests of a population proportion using a normal distribution (usually $n$ is large or the sample size is large).

If you are testing a single population mean , the distribution for the test is for means :

$\overline{X}$ ~ $N({\mu }_X,\frac{{\sigma }_X}{\sqrt{n}})$ or $t_{\text{df}}$

The population parameter is $\mu$ . The estimated value (point estimate) for $\mu$ is $\overline{x}$ , the sample mean.

If you are testing a single population proportion , the distribution for the test is for proportions or percentages:

$\mathrm{P\text{'}}$ ~ $N(p,\sqrt{\frac{p\cdot q}{n}})$

The population parameter is $p$ . The estimated value (point estimate) for $p$ is $\mathrm{p\text{'}}$ . $\mathrm{p\text{'}}=\frac{x}{n}$ where $x$ is the number of successes and $n$ is the sample size.