Answer
$0.47\gt Upper~bound$: null hypothesis is rejected.
There is enough evidence to conclude that parents’ attitudes toward the quality of education in the United States has changed since August 2002.
Work Step by Step
$p̂ =\frac{x}{n}=\frac{437}{1013}=0.4314$
Required condition:
$1013\times0.4314(1-0.4314)=1013\times0.4314(1-0.4314)=248.48\gt10$
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$z_{\frac{α}{2}}=z_{0.025}$
If the area of the standard normal curve to the right of $z_{0.025}$ is 0.025, then the area of the standard normal curve to the left of $z_{0.025}$ is $1−0.025=0.975$
According to Table V, the z-score which gives the closest value to 0.975 is 1.96.
$Lower~bound=p ̂-z_{\frac{α}{2}}.\sqrt {\frac{p ̂(1-p ̂)}{n}}=0.4314-1.96\times\sqrt {\frac{0.4314(1-0.4314)}{1013}}=0.4009$
$Upper~bound=p ̂+z_{\frac{α}{2}}.\sqrt {\frac{p ̂(1-p ̂)}{n}}=0.4314+1.96\times\sqrt {\frac{0.4314(1-0.4314)}{1013}}=0.4619$
Since $0.47\gt Upper~bound$ (out of the 95% confidence inerval), we reject the null hypothesis.
