Question

Your boss just came to you and said they had taken a simple random sample last year to determine the average age of season ticket holders across all 30 Major League Baseball teams. That sample comprised 950 respondents. The allowable error last year was +/- 4 years. Your boss was unsure of the variance associated with the population parameter and had no knowledge of the level of confidence associate with the measure. But, the degree of accuracy was deemed to be too high, so they want to run the sample again this season with an allowable error of half what it was last year. In other words, they need to double the accuracy such that the allowable error is +/- 2 years. What is the required size for your simple random sample?

Answer 1

answer is 3800

margin of error=z(alpha/2)*sd/sqrt(n) ( since sample size is large so we use z-value to find the margin of error)

now 4=z(alpha/2)*sd/sqrt(950)

or, sd=4*sqrt(950)/z(alpha/2)

now we want to find n such that

2=z(alpha/2)*sd/sqrt(n)

or, 2=z(alpha/2)*(4*sqrt(950)/z(alpha/2))/sqrt(n)

or, 2=4*sqrt(950)/sqrt(n)

or, sqrt(n)=4*sqrt(950)/2

or, sqrt(n)=2*sqrt(950)

or, n=4*950=3800

answer is 3800