For a random variable T that is T30 distributed Pr13 T 13

For a random variable T that is T(30) distributed, Pr[-1.3 < T < 1.3] = 0.80. Using this result, derive an 80% confidence interval for the population mean given a random sample with n = 31, u = 40, and s / n = 100

Solution

Thus,

lower bound = u - t *(s/sqrt(n)) = 40 - 1.3*100 = -90
upper bound = u + t *(s/sqrt(n)) = 40 + 1.3*100 = 170

Thus, the confidence interval is (-90, 170). [ANSWER]