A simple random sample of 49 8th graders at a large suburban middle school indicated that 88% of them are involved with some type of after school activity. Find the margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity.

The margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity is 0.0764.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

The margin of error is:

90% confidence level

So , z is the value of Z that has a p-value of , so .

A simple random sample of 49 8th graders at a large suburban middle school indicated that 88% of them are involved with some type of after school activity.

This means that

Margin of error:

The margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity is 0.0764.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a