Less than 23% of all homeowners have a security alarm. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
Begin by finding the alternative hypothesis for a hypothesis test of the claim. The null and alternative hypotheses are comprised of the claim its complement. The null hypothesis, is a statistical hypothesis that contain a statement of equality, whereas the alternative hypothesis, , contain a statement of strict inequality. In this case the alternative hypothesis is the claim.
: µ < 0.23
If the alternative hypothesis, , contain the less-than inequality symbol, (<), the hypothesis test is a left-tailed test, similarly, if it contain the greater-then inequality symbol, (>), it is a right-tailed test, and if is contain the not-equal-to symbol, (≠), it is a two-tailed test.
Since the alternative hypothesis : µ < 0.23 contain the less-than inequality symbol, the test is left-tailed.