Problem 401


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, H_{0} is a statistical hypothesis that contain a statement  of equality, whereas the alternative hypothesis, H{a} , contain a statement of strict inequality. In this case the alternative hypothesis is the claim.

H_{a}: µ < 0.23

If the alternative hypothesis, H_{a}, 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 H_{a}: µ < 0.23 contain the less-than inequality symbol, the test is left-tailed.


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