Question

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?

1) Left-tailed
2) Right-tailed
3) Two-tailed
4) Cannot be determined

Answer 1

The type of hypothesis test is determined by the alternative hypothesis. A not equals symbol (≠) in the alternative hypothesis indicates a two-tailed test, whereas the phrasing of the null hypothesis as 'at least' or 'at most' a certain value points to a left-tailed or right-tailed test, respectively.

Step-by-step explanation:

The type of hypothesis test (left-tailed, right-tailed, or two-tailed) is determined by the alternative hypothesis (Ha). When the alternative hypothesis includes a not equals symbol (≠), it indicates a two-tailed test. This means that the parameter being tested, usually a mean or proportion, could be different from the hypothesized value in either direction (greater than or less than).

For example, when the null hypothesis (H0) states that the mean is at least 18 and does not include the possibility of equality, then we have a left-tailed test. The parameter in question here is the mean of the population, and the test will look for evidence that the mean is less than 18. On the other hand, if H0 states that the mean is at most 12, this implies a right-tailed test where the test seeks evidence that the mean is greater than 12.