If the alternate hypothesis specifies a particular direction for the population parameter, it is appropriate to use:
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A. B. C. D.C
A one-tailed test is used when the alternate hypothesis specifies a particular direction for the population parameter.
In hypothesis testing, we evaluate a null hypothesis and an alternate hypothesis to make an inference about a population parameter based on sample data. The alternate hypothesis is a statement that contradicts or opposes the null hypothesis.
In this question, the key phrase is "specifies a particular direction for the population parameter." When the alternate hypothesis specifies a particular direction, it means we are interested in determining if the population parameter is either greater than or less than a certain value. In such cases, we use a one-tailed test.
A one-tailed test is used to test a hypothesis in a specific direction, either for an increase or a decrease in the population parameter. It allows us to focus the statistical analysis on one side of the distribution. In other words, it examines the evidence in favor of the hypothesis only in one direction.
Now, let's analyze the answer choices:
A. A z-statistic test: The z-statistic test refers to a test that uses the standard normal distribution. It can be used for hypothesis testing with a known population standard deviation. However, the z-test itself does not imply a specific direction for the alternate hypothesis, so it may not be the most appropriate choice in this case.
B. A stratified sampling test: Stratified sampling is a sampling technique used to divide a population into subgroups or strata and then draw samples from each stratum. It is not directly related to the type of hypothesis test being used. Therefore, this option is not applicable to the question.
C. A one-tailed test: As mentioned earlier, a one-tailed test is appropriate when the alternate hypothesis specifies a particular direction for the population parameter. It aligns with the requirement stated in the question and is the most suitable choice for this scenario.
D. A two-tailed test: A two-tailed test is used when the alternative hypothesis is two-sided, meaning it does not specify a particular direction. It tests whether the population parameter is different from the null hypothesis value in either direction. Since the question specifies a particular direction, a two-tailed test would not be appropriate in this case.
Based on the analysis above, the correct answer is C. a one-tailed test.