Question

for the following information, determine whether a normal sampling distribution can be used, where ( p ) is the population proportion, ( alpha ) 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 can be used here, since ( np geq 5 ) and ( nq geq 5 )
if a normal sampling distribution can be used, identify the hypotheses for testing the claim. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a. ( h_0: p < square, h_a: p geq square ) (round to two decimal places as needed.)
b. ( h_0: p geq square, h_a: p < square ) (round to two decimal places as needed.)
c. ( h_0: p
eq square, h_a: p = square ) (round to two decimal places as needed.)
d. ( h_0: p leq square, h_a: p > square ) (round to two decimal places as needed.)
e. ( h_0: p > square, h_a: p leq square ) (round to two decimal places as needed.)
f. ( h_0: p = square, h_a: p
eq square ) (round to two decimal places as needed.)
g. a normal sampling distribution cannot be used

Explanation:

Step1: Identify the claim

The claim is \( p\geq0.47 \).

Step2: Determine the null and alternative hypotheses

The null hypothesis \( H_{0} \) is the statement of equality. The alternative hypothesis \( H_{a} \) is the statement that we are trying to find evidence for.
For a claim of \( p\geq0.47 \), the null hypothesis \( H_{0}:p\leq0.47 \) (the opposite of the claim for the equality - based null hypothesis) and the alternative hypothesis \( H_{a}:p > 0.47 \)

Answer:

D. \( H_{0}:p\leq0.47\), \(H_{a}:p > 0.47\)