Final answer:
To construct a confidence interval at a 80% confidence level, we use the formula: CI = x-bar ± (Z * (s / sqrt(n))). In this case, n = 29, x-bar = 31, s = 14, and the desired confidence level is 80%, which corresponds to a Z-score of 1.28. The confidence interval is (28.48, 33.52), meaning we are 80% confident that the true population mean lies within this interval.
Step-by-step explanation:
To construct a confidence interval at a 80% confidence level, we use the formula:
CI = x-bar ± (Z * (s / sqrt(n)))
where CI is the confidence interval, x-bar is the sample mean, s is the standard deviation, n is the sample size, and Z is the Z-score corresponding to the desired confidence level.
In this case, n = 29, x-bar = 31, s = 14, and the desired confidence level is 80%, which corresponds to a Z-score of 1.28. Plugging these values into the formula, we get:
CI = 31 ± (1.28 * (14 / sqrt(29)))
Simplifying, we calculate the confidence interval to be (28.48, 33.52). Therefore, we are 80% confident that the true population mean lies within the interval of (28.48, 33.52).