A financial analyst claims that the return rate of a 15-year bond has a standard deviation of 7.1%. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
Solution
Begin by finding alternative hypothesis for a hypothesis test of the claim. The null and alternative hypothesis are comprised of the claim and its complement. The null hypothesis, 
, is a statistical hypothesis that contains a statement of equality, whereas the alternative hypothesis, 
: contain a statement of strict inequality. In this case the alternative hypothesis is the complement of the claim.
: σ ≠ 0.071
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 it contain the not-equal-to symbol,(≠), it is a two-tailed test.
Since the alternative hypothesis : σ ≠ 0.071 contain the not-equal to symbol, the test is two-tailed.