Reading proficiency: An educator wants to construct a 99.5% confidence interval for the proportion of elementary school children in Colorado who are proficient in reading.

The results of a recent statewide test suggested that the proportion is 0.69.

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?

A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

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 zscore that has a pvalue of .

The margin of error of the interval is given by:

In this problem, we have that:

99.5% confidence level

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

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?

This is n when M = 0.07. So

A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

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step-by-step explanation: