Question

test the hypothesis using the p - value approach. be sure to verify the requirements of the test
$h_0: p = 0.2$ versus $h_1: p>0.2$
$n = 125$, $x = 40$, $\alpha=0.1$
is $np_0(1 - p_0)\geq10$?
no
yes
use technology to find the p - value.
$p - value=\square$
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$. Given $x = 40$ and $n=125$, so $\hat{p}=\frac{40}{125}=0.32$.

Step2: Calculate the test - statistic

The test - statistic for a one - sample proportion test is $z=\frac{\hat{p}-p_{0}}{\sqrt{\frac{p_{0}(1 - p_{0})}{n}}}$.
Substitute $p_{0}=0.2$, $\hat{p}=0.32$, and $n = 125$ into the formula:

$$
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$$

Step3: Find the P - value

Since the alternative hypothesis is $H_{1}:p>0.2$ (right - tailed test), the P - value is $P(Z>z)$.
Using a standard normal table or technology (e.g., in Excel: =1 - NORM.S.DIST(3.35, TRUE)), we find that the P - value is approximately $0.0004$.

Answer:

$0.000$ (rounded to three decimal places)