statistics

The minimum sample size needed here would be based on the confidence interval formula, where the researcher desires a 95% confidence level that the sample mean age is within 1.5 years of the population mean age. The necessary sample size (n) can be calculated using the following formula: n > [(z-value for 95% confidence level)2 x (population standard deviation)]2 / (desired error margin)2 Substituting the given values, we will get the following formula: n > [(1.96)2 x (8)2] / (1.5)2 This simplifies to n > 514.7, so the minimum sample size needed is 515. In conclusion, the researcher will need to sample at least 515 people in order to obtain the desired 95% confidence level that the sample mean age is within 1.5 years of the population mean age.