Question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed. H: H=78 H: A < 78 A) two-tailed B) left-tailed C) right-tailed

Answer 1

Solution: In the given question, the null and alternative hypotheses are written as:

H0: $\mu$ = 78 vs H1: $\mu$ < 78

By definition, we know in Statistical Hypothesis testing, the alternative hypothesis can be of three types.

i) Left-tailed test -- It is the one where the rejection region is located to the extreme left of the distribution. This test is conducted when the alternative hypothesis contains the condition "H1: parameter < k (a particular quantity)".

ii) Rlight-tailed test -- It is the one where the rejection region is located to the extreme right of the distribution. This test is conducted when the alternative hypothesis contains the condition "H1: parameter > k (a particular quantity)".

iii) Two-tailed test -- It is the test where the rejection region is divided between two critical values at the extremities of the distributin, symmetrically. The alternative hypothesis is of the form "H1: parameter $\neq$ k (a particular quantity)"

Thus, here H1: $\mu$ < 78, matches with the first type, i.e. a left-tailed.

Hence, option (B) left-tailed is the correct option.