Question

An economist would like to estimate the 99% confidence interval for the average real estate taxes collected by a small town in California. In a prior analysis, the standard deviation of real estate taxes was reported as $1,470. [You may find it useful to reference the z table.] What is the minimum sample size required by the economist if he wants to restrict the margin of error to $510

Answer 1

Solution :

Given that,

standard deviation = = $1470

margin of error = E = $510

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 1470) / 510)²

= 55.1 = 55

minimum Sample size = 55