Question

The following gives information about the proportion of a sample that agree with a certain statement. Use StatKey or other technology to find a confidence interval at the given confidence level for the proportion of the population to agree, using percentiles from a bootstrap distribution. StatKey tip: Use ‘‘CI for Single Proportion" and then ‘‘Edit Data" to enter the sample information.Find a 90% confidence interval if 112 agree and 288 disagree in a random sample of 400 people.What is the 90% confidence interval? ________, ________

Answer 1

Answer:

(0.2278, 0.3322)

Step-by-step explanation:

Given that out of 400 people 112 agree and 288 disagree

Proportion of people agreeing = $\frac{112}{400} =0.28$

$q=1-p =0.72\\se = \sqrt{\frac{pq}{n} } =0.03175$

For confidence interval 90% we have critical value as

1.645

Margin of error =1.645*SE

=$1.645(0.03175)\\= 0.0522$

Confidence interval $= (0.28-0.0522, 0.28+0.0522)\\= (0.2278, 0.3322)$