Final answer:
The question involves a left-tailed hypothesis test in statistics, evaluating whether the population mean (μ) is less than a certain value based on the significance level (alpha). A test statistic is calculated and compared to critical values to decide whether to reject the null hypothesis, using p-value comparisons with alpha.
Step-by-step explanation:
The question pertains to a hypothesis test in statistics, which is a method used to make inferences about the population mean (μ) based on sample data. The null hypothesis (H0) states that the population mean is equal to a specific value (H0: μ = 73.4), while the alternative hypothesis (Ha) suggests that the population mean is less than a specific value (Ha: μ < 69.2). This is a one-tailed left-tailed hypothesis test.
To conduct this test, one would typically calculate a test statistic based on the sample data, compare it to a critical value that corresponds to the given significance level (alpha = 0.002), and determine whether to reject or fail to reject the null hypothesis. If the test statistic falls into the critical region (typically, if it is less than the critical value), we reject the null hypothesis, indicating support for the alternative hypothesis. If the test statistic does not fall into the critical region, we fail to reject the null hypothesis, indicating insufficient evidence to support the alternative hypothesis.
To make the decision of whether to reject H0 or not, one would compare the p-value obtained from the test statistic to the significance level (α). If the p-value is less than α, the null hypothesis is rejected in favor of the alternative hypothesis.