An educator wants to estimate the proportion of school children in Boston who are living with only one parent. Since their report is to be published, they want a reasonably accurate estimate. However, since their funding is limited, they do not want to collect a larger sample than necessary. They hope to use a sample size such that, with probability 0.95, the error will not exceed 0.04. What sample size will ensure this, regardless of what sample proportion value occurs when they gather the sample?

Question

An educator wants to estimate the proportion of school children in Boston who are living with only one parent.  Since their report is to be published, they want a reasonably accurate estimate.  However, since their funding is limited, they do not want to collect a larger sample than necessary.  They hope to use a sample size such that, with probability 0.95, the error will not exceed 0.04.  What sample size will ensure this, regardless of what sample proportion value occurs when they gather the sample?

MathGuru · Answer

Try this formula:
n = [(z-value)^2 * p * q]/E^2

Note: n = sample size needed; .5 for p and .5 for q are used if no value is stated in the problem. E = maximum error, which is .04 in the problem. Z-value is found using a z-table (for 95%, the value is 1.96).

MathGuru · Answer

When you find n, round up to the next highest whole number.