Solution: In the given question, the null and alternative hypotheses are written as:
H0: = 78 vs H1: < 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 k (a particular quantity)"
Thus, here H1: < 78, matches with the first type, i.e. a left-tailed.
Hence, option (B) left-tailed is the correct option.
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