Answer:
82%
Step-by-step explanation:
Find attached solution to problem below.
The value of c is 82%.
A newspaper reporter asked an SRS of 100 residents in a large city for their opinion about the mayor's job performance.
Using the results from the sample, the C% confidence interval for the proportion of all residents in the city who approve of the mayor's job performance is 0.565 to 0.695.
What is the value of c?
The sample space n = 100
And the confidence interval is 0.565 to 0.695.
Then,
The confidence interval of the =all residents in the city who approve of the mayor's job performance is 0.565 to 0.695 is,
[tex]\rm p = \dfrac{0.565+0.695}{2}\\ \\ p = \dfrac{1.260}{2}\\ \\ p= 0.63[/tex]
Then,
The confidence interval is given by,
[tex]\rm Confidence \ interval = p\pm Z_{\frac{\alpha}{2}} \times \sqrt{\dfrac{p(1-p)}{n}}\\ \\ 0.695= 0.63\pm Z_{\frac{\alpha}{2}} \times \sqrt{\dfrac{0.63(1-0.63)}{100}}\\ \\ 0.695-0.63=Z_{\frac{\alpha}{2}} \times \sqrt{\dfrac{0.63\times 0.37}{100}}\\\\ 0.065 = Z_{\frac{\alpha}{2}} \times \sqrt{\dfrac{0.2331}{100}} = 0.065 = Z_{\frac{\alpha}{2}} \times \sqrt{0.002331} \\\\ 0.065 = Z_{\frac{\alpha}{2}} \times 0.4828\\ \\ \dfrac{0.065}{0.4828} = Z_{\frac{\alpha}{2}} \\ \\ Z_{\frac{\alpha}{2}}=1.35 [/tex]
Therefore,
the value of c is.
[tex]\rm Confidence\ interval = P(-1.35
Hence, the value of c is 82%.
To know more about Confidence intervals click the link given below.
https://brainly.com/question/3041663
