1215

Based on Student's t-distribution, 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) -0.851% to 8.851%.

B) 1.261% to 6.739%.

C) -0.794% to 8.794%.

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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% confidence and df = 40, the critical t-value is 2.021. Therefore the 95% confidence interval is approximately: 4% ± 2.021(2.372) or 4% ± 4.794% or -0.794% to 8.794%.

1215

The approximate 99% confidence interval for the population mean based on a sample of 60 returns with a mean of 7% and a sample standard deviation of 25% is closest to:

A) -1.584% to 15.584%.

B) 1.584% to 14.584%.

C) 0.546% to 13.454%.

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The standard error for the mean = s / (n)^0.5 = 25% / (60)^0.5 = 3.227%. The critical value from the t-table should be based on 60 ? 1 = 59 df. Since the standard tables do not provide the critical value for 59 df the closest available value is for 60 df. This leaves us with an approximate confidence interval. Based on 99% confidence and df = 60, the critical t-value is 2.660. Therefore the 99% confidence interval is approximately: 7% ± 2.660(3.227) or 7% ± 8.584% or -1.584% to 15.584%.

If you use a z-statistic, the confidence interval is 7% ± 2.58(3.227) = -1.326% to 15.326%, which is closest to the correct choice.