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 215 of 850 parents of children in high school felt it was a serious problem. 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 } = - 10.70 ) (round to two decimal places as needed)
find the p - value.
p - value = (round to three decimal places as needed)

Explanation:

Step1: <Determine the P - value formula>

For a two - tailed z - test, the P - value is \(P = 2\times(1 - \Phi(|z_0|))\), where \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution and \(z_0=- 10.70\).

Step2: <Find the P - value>

Since \(|z_0| = 10.70\), and for \(z = 10.70\), the value of \(\Phi(10.70)\approx1\) (because for large \(z\) values, the standard normal cumulative distribution function approaches 1). Then \(P=2\times(1 - 1)=0\)

Answer:

\(0.000\)