Question

for the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, α is the level of significance, \\( \hat { p } \\) is the sample proportion, and n is the sample size. if it can be used, test the claim. claim: \\( p \geq 0.47, \alpha = 0.04 \\). sample statistics: \\( \hat { p } = 0.40, n = 120 \\) let \\( q = 1 - p \\) and let \\( \hat { q } = 1 - \hat { p } \\). a normal sampling distribution \\( \square \\) be used here since \\( \square \square 5 \\) and \\( \square \square 5 \\)

Explanation:

Step1: Check \(np\)

Calculate \(np = 120\times0.47=56.4\). Since \(56.4>5\).

Step2: Check \(nq\)

First, \(q = 1 - p=1 - 0.47 = 0.53\). Then \(nq=120\times0.53 = 63.6\). Since \(63.6>5\).

Answer:

A normal sampling distribution can be used here since \(np>5\) and \(nq>5\).