1215

From a sample of 41 monthly observations of the S& Mid-Cap index, the mean monthly return is 1% and the sample variance is 36. For which of the following intervals can one be closest to 95% confident that the population mean is contained in that interval?

A) 1.0% ± 1.9%.

B) 1.0% ± 6.0%.

C) 1.0% ± 1.6%.

---

If the distribution of the population is nonnormal, but we don’t know the population variance, we can use the Student’s t-distribution to construct a confidence interval. The sample standard deviation is the square root of the variance, or 6%. Because there are 41 observations, the degrees of freedom are 40. From the Student’s t distribution, we can determine that the reliability factor for t_0.025, is 2.021. Then the 95% confidence interval is 1.0% ± 2.021(6 / √41) or 1.0% ± 1.9%.

1215

A random sample of 25 Indiana farms had a mean number of cattle per farm of 27 with a sample standard deviation of five. Assuming the population is normally distributed, what would be the 95% confidence interval for the number of cattle per farm?

A) 23 to 31.

B) 25 to 29.

C) 22 to 32.

---

The standard error of the sample mean = 5 / √25 = 1
Degrees of freedom = 25 ? 1 = 24
From the student’s T table, t_5/2 = 2.064
The confidence interval is: 27 ± 2.064(1) = 24.94 to 29.06 or 25 to 29.