Question

twenty years ago, 53% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. a recent survey found that 295 of 850 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. do parents feel differently today than they did twenty years ago? use the α = 0.1 level of significance
because ( n p _ { 0 } ( 1 - p _ { 0 } ) = 211.7 > 10 ), the sample size is less than 5% of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied
(round to one decimal place as needed)
what are the null and alternative hypotheses?
( h _ { 0 } : p = 0.53 ) versus ( h _ { 1 } : p
eq 0.53 )
(type integers or decimals. do not round.)
find the test statistic.
( z _ { 0 } = square ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is given by $\hat{p}=\frac{x}{n}$, where $x = 295$ and $n=850$.
So, $\hat{p}=\frac{295}{850}\approx0.347$.

Step2: Calculate the test - statistic formula

The formula for the test - statistic $z_0$ in a one - sample proportion test is $z_0=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$.
Here, $p_0 = 0.53$, $\hat{p}\approx0.347$, and $n = 850$.
First, calculate the denominator:
$\sqrt{\frac{0.53\times(1 - 0.53)}{850}}=\sqrt{\frac{0.53\times0.47}{850}}=\sqrt{\frac{0.2491}{850}}\approx\sqrt{0.000293}\approx0.0171$.
Then, calculate the numerator: $\hat{p}-p_0=0.347 - 0.53=-0.183$.
Now, calculate $z_0$:
$z_0=\frac{-0.183}{0.0171}\approx - 10.70$.

Answer:

$z_0\approx - 10.70$