QuestionEyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a given time period and found that $12 \%$ of all lenses had defects of some type. Looking at the type of defects, they found in a three-month time period that out of 34,054 defective lenses, 4257 were due to scratches. Are there more defects from scratches than from all other causes? Use a $1 \%$ level of significance.
State the hypotheses. $H_{0}: p$ ? $\square$ $H_{a}: p ?$ $\square$ Calculate the test statistic. Round to four decimal places. $$\hat{p}=$$ $\square$ Calculate the standardized test statistic. Round to three decimal places. $$z=\square$$
Find the $p$-value. Round to four decimal places. $p$-value $=$ $\square$ State your decision. Since the $p$-value is greater than .01 , fail to reject $H_{0}$. Since the $p$-value is greater than .01 , reject $H_{0}$. Since the $p$-value is less than .01 , reject $H_{0}$. Since the $p$-value is less than .01 , fail to reject $H_{0}$.
Interpret the results. At the $1 \%$ level of significance, there is enough evidence to show that the proportion of defective lenses from scratches is lower than $12 \%$, the proportion from other causes. At the $1 \%$ level of significance, there is enough evidence to show that the proportion of defective lenses from scratches is higher than $12 \%$, the proportion from other causes. At the $1 \%$ level of significance, there is not enough evidence to show that the proportion of defective lenses from scratches is lower than $12 \%$, the proportion from other causes. At the $1 \%$ level of significance, there is not enough evidence to show that the proportion of defective lenses from scratches is higher than $12 \%$, the proportion from other causes. At the $1 \%$ level of significance, there is not enough evidence to show that the proportion of defective lenses from scratches is not equal to $12 \%$, the proportion from other causes.