Question

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 550 comma x equals 440 comma 95 % confidence nothingless thanpless than nothing ​(Round to three decimal places as​needed.)

Answer 1

Answer:

(0.767,0.833)

Step-by-step explanation:

The 95% confidence interval for population proportion p can be computed as

$p-z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} } <P<p+z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }$

The z-value associated with 95% confidence level is 1.96.

whereas p=x/n

We are given that x=440 and n=550.

p=440/550=0.8

$0.8-1.96\sqrt{\frac{0.8(0.2)}{550} } <P<0.8+1.96\sqrt{\frac{0.8(0.2)}{550} }$

$0.8-1.96\sqrt{\frac{0.16}{550} } <P<0.8+1.96\sqrt{\frac{0.16}{550} }$

$0.8-1.96\sqrt{0.00029 } <P<0.8+1.96\sqrt{0.00029 }$

$0.8-1.96(0.01706) <P<0.8+1.96(0.01706)$

$0.8-0.03343 <P<0.8+0.03343$

$0.76657 <P<0.83343$

Thus, the required confidence interval is

0.767<P<0.833  (rounded to 3 decimal places)

Hence, we are 95% confident that our true population proportion will lie in the interval (0.767,0.833)