Question

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

Explanation:

To reject \(H_0: p\geq0.45\), the confidence interval should not contain any values greater than or equal to \(0.45\).

• For option A: The interval \((0.32,0.40)\) has all values less than \(0.45\).
• For option B: The interval \((0.40,0.50)\) contains values greater than \(0.45\) (e.g., \(0.46,0.47,\cdots,0.50\)).
• For option C: The interval \((0.42,0.47)\) contains values greater than \(0.45\) (e.g., \(0.46,0.47\)).

Answer:

A. \((0.32,0.40)\)