Final answer:
In a two-tailed hypothesis test, any approaches involving the alternative hypothesis containing an equal sign cannot be used. The test involves collecting data and using either p-values or critical values to make a decision about the null hypothesis, with the Ha indicating differences in both directions.
Step-by-step explanation:
For a two-tailed hypothesis test, you cannot use an approach with an alternative hypothesis symbol that contains an equal sign. When conducting hypothesis testing, there are typically two types of errors that we try to minimize: Type I errors (rejecting a true null hypothesis) and Type II errors (failing to reject a false null hypothesis). For a two-tailed hypothesis test, we are concerned with significant differences in both directions from the hypothesized mean, either higher or lower. The approaches you can use for a two-tailed hypothesis test include a test of two proportions, a test of two independent means, a test of a single mean, or a test of matched pairs. These approaches involve setting up two contradictory hypotheses, collecting sample data, determining the correct distribution, and analyzing sample data to make a decision on the null hypothesis.
These methods include the use of p-values or critical values to determine whether to reject or not reject the null hypothesis. The p-value method allows for flexibility in choosing a significance level, whereas the critical value method typically uses a standard significance level, often 0.05 unless specified otherwise. The alternative hypothesis (Ha) for a two-tailed test will have a 'not equals' symbol (≠) to indicate that the test is looking for differences in both directions.