Calculate the lower confidence limit (LCL) and upper confidence limit (UCL) of the mean for each of the following.a. x =265, n=459, σ=50, and α=0.01b. x=180, n=308, σ2equals=100, and α=0.05LCLequals=(Round to two decimal places as needed.)UCLequals=(Round to two decimal places as needed.)b.LCLequals=(Round to two decimal places as needed.)UCLequals=(Round to two decimal places as needed.)
Accepted Solution
A:
Answer:a: 258.09b: 178.88Step-by-step explanation:For a: Since n > 30, we use a z-value that corresponds to 0.01, or 99% confidence. This z-value is: 2.575We have: x = 265, n = 459, σ = 50. See the calculation for the error and the construction of the confidence interval on the first attached photoFor b: Since n > 30, we use a z-value that corresponds to 0.05, or 95% confidence. This z-value is: 1.96x = 180, n = 308, σ = 10 (it gives σ² = 100. so σ = 10). See the calculation for the error and the construction of the confidence interval on the second attached photo