Express the confidence interval 53.5%&lt;p&lt;69.7% in the form of p^±MEp^±ME

Answered: "Express the confidence interval 53.5%<p<69.7% in the form..."

Efan Halliday

Answered question

2021-09-23

Express the confidence interval $53.5 % < p < 69.7 %$ in the form of $\hat{p} \pm M E \hat{p} \pm M E$

Answer & Explanation

faldduE

Skilled2021-09-24Added 109 answers

Step 1
Solution
Given:
Confidence interval in the trilinear inequality form:
Lower limit $< p <$ Upper limit
$53.5 % < p < 69.7 %$
Hence,
Lower limit $= 53.5 %$
Upper limit $= 69.7 %$
Step 2
Sample proportion $(\hat{p}) = \frac{Upper limit+Lower limit}{2}$
Plug in all the values in the formula, we get
Simple proportion $(\hat{p}) = \frac{69.7 % + 53.5 %}{2}$
Sample proportion $(\hat{p}) = 61.6 %$
Step 3
Margin of error $(M E) = \frac{Upper limit+Lower limit}{2}$
Plug in all the values in the formula, we get
Margin of error $(M E) = \frac{69.7 % + 53.5 %}{2}$
Margin of error $(M E) = 8.1 %$
Step 4
Express the confidence interval in the form $(\hat{p}) \pm E$
$(\hat{p}) \pm E - 61.6 % \pm 8.1 %$

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