quiz 2sd confidence intervals categorical variable

A statistical study was completed resulting in a
$\hat{p}$ of 0.687. The sample size was
$n=128$. Use this information to answer the next 2 questions. Use the formula
$\hat{p}Â\pm 2×\sqrt{\frac{\hat{p}(1−\hat{p}}{n}}$.

1. What is the margin-of-error for a 2SD confidence interval? Round to 3 decimal places. Use this value for the next two questions.

2. What is the lower bound of the 2SD 95% CI? Use the MOE from the previous question. Round to 3 decimal places.

3. What is the upper bound of the 2SD 95% CI? Use the rounded MOE from 2 questions back. Round to 3 decimal places.

A 95% CI constructed using the 2SD method is (0.4562,0.5614). Work backwards to deconstruct this CI to answer the next 3 questions using this. There is a problem similar to this in the notes.

1. What is the value of
$\hat{p}$ ? Round to 4 decimal places.

2. What is the margin-of-error? Round to 4 decimal places.

3. What is the value of the SE of
$\hat{p}$? Round to 4 decimal places.

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