Question

Express the confidence interval 0.111 < p < 0.777  in the form ^ p± Ep ^±E.

Answer 1

Answer:

$0.111 < p < 0.777$

And we know that this interval is calculated from this formula:

$\hat p \pm E$

Where E represent the margin of error given by:

$ME= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

And we can calculate the sampel proportion with this operation:

$\hat p=\frac{0.111+0.777}{2}= 0.444$

And the error can be calculated as:

$E=\frac{0.777-0.111}{2}= 0.333$

And the confidence interval would be given by:

$0.444 \pm 0.333$

Step-by-step explanation:

For this case we have the following interval given:

$0.111 < p < 0.777$

And we know that this interval is calculated from this formula:

$\hat p \pm E$

Where E represent the margin of error given by:

$ME= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

And we can calculate the sampel proportion with this operation:

$\hat p=\frac{0.111+0.777}{2}= 0.444$

And the error can be calculated as:

$E=\frac{0.777-0.111}{2}= 0.333$

And the confidence interval would be given by:

$0.444 \pm 0.333$