A magarine provided resulis from a poll of 1000 adiths who were asked to identhy their favorte pie. Fmong the 1000 responderis, \( 11 \% \) choce choculate pie, and the margin of points. What values do \( \hat{D}, \hat{a}, n, E \), and \( p \) represent? it the contidence level is \( 90 \% \), what is the value of of The value of \( \hat{p} \) is the sample proportion. The vatue of ig is found from evaluating \( 1-\hat{i} \) The value of \( n \) is the sample size. The valus of E is the margin of error. The value of \( p \) is the popalation propotion. It the confidence level is \( 95 \% \), what is the value of of \( a= \) \( \square \) (Type an integer or a decimal. Do not round)

To clarify the meaning of the symbols you're working with: \( \hat{D} \) generally represents the difference in sample proportions, while \( \hat{p} \) is the sample proportion—in this case, \( 11\% \) of the 1000 respondents chose chocolate pie, making \( \hat{p} = 0.11 \). The sample size, \( n \), is the total number surveyed: \( n = 1000 \). The margin of error \( E \) is a crucial component in estimating how accurate your sample proportion could be against the true population parameter. The value of \( p \) signifies the true population proportion. When it comes to confidence intervals, the value of \( \alpha \) (alpha) is calculated as \( 1 - \text{confidence level} \). So for a 95% confidence level, \( \alpha = 0.05 \), meaning there's a 5% chance that your confidence interval does not capture the true population parameter.