If you wish to test whether population mean is lower than some hypothesized value, you would apply:

Correct option is A

To test whether the population mean is lower than a hypothesized value, you would use a one-tailed test. In hypothesis testing, a one-tailed test is used when the research hypothesis predicts a specific direction of the effect (either less than or greater than a certain value). In this case, the null hypothesis (H₀) might state that the population mean is equal to or greater than the hypothesized value, while the alternative hypothesis (H₁) would state that the population mean is less than the hypothesized value. By using a one-tailed test, you focus on the probability of observing data in one direction, which increases the test's power to detect an effect in that direction.
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Two-tailed test: (b) A two-tailed test is used when the research hypothesis does not predict the direction of the effect, only that there is an effect (i.e., the population mean is different from the hypothesized value). It tests for deviations in both directions (greater than or less than).
Hall-tailed test: (c) There is no such statistical test known as a hall-tailed test. This option is incorrect.
Three-tailed test: (d) There is no such statistical test known as a three-tailed test. This option is also incorrect.