We began this chapter by learning about the two hypotheses that make up the structure of a hypothesis test. The null hypothesis is the statement being tested. Usually it represents the status quo and it is not rejected unless there is convincing sample evidence that it is false. The alternative, or, research, hypothesis is a statement that is accepted only if there is convincing sample evidence that it is true and that the null hypothesis is false. In some situations, the alternative hypothesis is a condition for which we need to attempt to find supportive evidence. We also learned that two types of errors can be made in a hypothesis test. A Type I error occurs when we reject a true null hypothesis, and a Type II error occurs when we do not reject a false null hypothesis.

We studied two commonly used ways to conduct a hypothesis test. The first involves comparing the value of a test statistic with what is called a rejection point, and the second employs what is called a p -value. The p -value measures the weight of evidence against the null hypothesis. The smaller the p -value, the more we doubt the null hypothesis. We learned that, if we can reject the null hypothesis with the probability of a Type I error equal to <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/fish.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>, then we say that the test result has statistical significance at the <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/fish.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> level. However, we also learned that, even if the result of a hypothesis test tells us that statistical significance exists, we must carefully assess whether the result is practically important. One good way to do this is to use a point estimate and confidence interval for the parameter of interest.

The specific hypothesis tests we covered in this chapter all dealt with a hypothesis about one population parameter. First, we studied a test about a population mean that is based on the assumption that the population standard deviation <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/sigma.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> is known. This test employs the normal distribution. Second, we studied a test about a population mean that assumes that <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0072977477/302316/sigma.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> is unknown. We learned that this test is based on the t distribution. Figure 8.19 presents a flowchart summarizing how to select an appropriate test statistic to test a hypothesis about a population mean. Then we presented a test about a population proportion that is based on the normal distribution. Next (in optional Section 8.6) we studied Type II error probabilities, and we showed how we can find the sample size needed to make both the probability of a Type I error and the probability of a serious Type II error as small as we wish. We concluded this chapter by discussing (in optional Sections 8.7 and 8.8) the chi-square distribution and its use in making statistical inferences about a population variance.