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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1)...

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Determine whether t

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
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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.

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