Question: What is meant by 95% confidence interval of the mean?
A ) 95% of the specific sample means will fall within ± 1.96 standard errors of the population mean. B ) 95% of the specific sample means will fall within ± 2.58 standard errors of the population mean. C ) There is 95% probability that the sample mean is equal to the actual population mean. D ) standard deviation of the population mean = 5
Steps to derive
1 When the sample size is large, approximately 95% of the sample mean will fall within ± 1.96 standard errors of the population mean. [Central limit theorem.]
2 Value of 1.96 corresponds to 95% confidence level taken from standard table of the t distribution.
