Problem
6 Question 19, 7.3.14-T HW Score: $38.01 \%, 11.4$ of Su points Part 1 of 4 Points: 0 of 1 Sa Use technology and a t-test to test the claim about the population mean $\mu$ at the given level of significance $\alpha$ using the given sample statistics. Assume the population is normally distributed. Claim: $\mu>72 ; \alpha=0.01$ Sample statistics: $\bar{x}=75.9, s=3.5, n=23$ What are the null and alternative hypotheses? Choose the correct answer below. A. \[ \begin{array}{l} H_{0}: \mu \geq 72 \\ H_{A}: \mu<72 \end{array} \] c. \[ \begin{array}{l} H_{0}: \mu \leq 72 \\ H_{A}: \mu>72 \end{array} \] B. \[ \begin{array}{l} H_{0}: \mu=72 \\ H_{A} \mu \neq 72 \end{array} \] D. \[ \begin{array}{l} H_{0}: \mu \neq 72 \\ H_{A}: \mu=72 \end{array} \]
Solution
Step 1 ：The null hypothesis (H0) is a statement of no effect or no difference and is the assumption that any kind of difference or importance you see in a set of data is due to chance. The alternative hypothesis (HA) is a statement of what a statistical hypothesis test is set up to establish.
Step 2 ：In this case, the claim is that the population mean is greater than 72 (μ > 72). This is our alternative hypothesis. The null hypothesis is the statement that the population mean is less than or equal to 72 (μ ≤ 72).
Step 3 ：Therefore, the correct answer should be: \(H_{0}: \mu \leq 72 \) and \(H_{A}: \mu>72 \)
Step 4 ：Final Answer: \(\boxed{H_{0}: \mu \leq 72, H_{A}: \mu>72}\)
