Question

given ( h_0:pgeq0.45 ), for which confidence interval should you reject ( h_0 )?
o a. ( (0.42,0.47) )
o b. ( (0.40,0.50) )
o c. ( (0.32,0.40) )

Explanation:

Step1: Understand the null hypothesis

The null hypothesis \(H_0:p\geq0.45\) means we expect the population proportion \(p\) to be at least \(0.45\).

Step2: Check each confidence interval

• For option A: The interval \((0.42,0.47)\) contains values \(\geq0.45\) (e.g., \(0.47\)), so we do not reject \(H_0\).
• For option B: The interval \((0.40,0.50)\) contains values \(\geq0.45\) (e.g., \(0.50\)), so we do not reject \(H_0\).
• For option C: The interval \((0.32,0.40)\) has all values less than \(0.45\). Since the entire confidence interval is below \(0.45\), it contradicts the claim \(p\geq0.45\) in \(H_0\).

Answer:

C. \((0.32,0.40)\)