"A simple random sample of 49 8th graders at a large suburban middle school indicated that 84% of them are involved with some type of after school activity. Find the margin of error associated with a 98% confidence interval that estimates the proportion of them that are involved in an after school activity."'

The margin of error associated with a 98% confidence interval that estimates the proportion of them that are involved in an after school activity is of 0.1219.

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 of:

A simple random sample of 49 8th graders at a large suburban middle school indicated that 84% of them are involved with some type of after school activity.

This means that

98% confidence level

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

Margin of error:

The margin of error associated with a 98% confidence interval that estimates the proportion of them that are involved in an after school activity is of 0.1219.

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