Let's go through each of the variables in this question:

1. Sample Proportion ($\hat{p}$): This represents the proportion of respondents who chose chocolate pie. Since 11% of 1500 respondents chose chocolate pie, $\hat{p} = 0.11$.

2. Complement of Sample Proportion ($\hat{q}$): This is calculated as $1 - \hat{p}$, which represents the proportion of respondents who did not choose chocolate pie. So, $\hat{q} = 1 - 0.11 = 0.89$.

3. Sample Size ($n$): This is the total number of respondents in the survey, which is given as $n = 1500$.

4. Margin of Error (E): The margin of error is given as $\pm 5\%$, so $E = 0.05$.

5. Significance Level ($\alpha$): The confidence level is 90%, which means the significance level $\alpha$ is $1 - 0.90 = 0.10$.

Summary of Answers:

• The value of $\hat{p}$ is 0.11
• The value of $\hat{q}$ is 0.89
• The value of $n$ is 1500
• The value of $E$ is 0.05
• The value of $\alpha$ is 0.10

Would you like a deeper explanation on any part?

Here are some related questions for further practice:

1. How would the values change if the confidence level was 95%?
2. What is the formula for calculating the margin of error in a confidence interval?
3. How is the sample proportion different from the population proportion?
4. How does increasing the sample size affect the margin of error?
5. What confidence level would correspond to a significance level of 0.05?

Tip: When calculating confidence intervals, remember that the margin of error is based on both the sample proportion and the sample size.