why did they use t-statistic? I had used 1.96 as the reliability factor and got the wrong answer! The 95% confidence interval for the population mean based on a sample of 40 interest rates with a sample mean of 4% and a sample standard deviation of 15% is closest to: A) -0.794% to 8.794%. B) -0.851% to 8.851%. C) 1.261% to 6.739%. D) 1.851% to 9.851%. Your answer: A was correct! The standard error for the mean = s/(n)0.5 = 15%/(40)0.5 = 2.372%. The critical value from the t-table should be based on 40 – 1 = 39 df. Since the standard tables do not provide the critical value for 39 df the closest available value is for 40 df. This leaves us with an approximate confidence interval. Based on 95 percent confidence and df = 40, the critical t-value is 2.021. Therefore the 95 percent confidence interval is approximately: 4% ± 2.021(2.372) or 4% ± 4.794% or -0.794% to 8.794%.
Both are correct, but since they asked for the closest, you would choose A, as you did.