Question

check here for instructional material to complete this problem.
evaluate the formula ( z=\frac{hat{p}-p}{sqrt{\frac{p q}{n}}} ) when ( hat{p}=\frac{287}{1024}, n = 1024, p = 0.30 ), and ( q = 1 - p ).
( z=quad ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate $\hat{p}$

$\hat{p}=\frac{287}{1024}\approx0.28$

Step2: Calculate $q$

Since $q = 1 - p$ and $p=0.30$, then $q=1 - 0.30=0.70$

Step3: Calculate the denominator $\sqrt{\frac{pq}{n}}$

Substitute $p = 0.30$, $q = 0.70$ and $n = 1024$ into $\sqrt{\frac{pq}{n}}$:

$$
LATEXBLOCK0
$$

Step4: Calculate $z$

Substitute $\hat{p}\approx0.28$, $p = 0.30$ and the value of the denominator $\approx0.0143$ into $z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}$:

$$
LATEXBLOCK1
$$

Answer:

$-1.40$