Please check my work. Calculate and interpret 95% and 99% confidence intervals f
ID: 3049759 • Letter: P
Question
Please check my work. Calculate and interpret 95% and 99% confidence intervals for the population mean household income. I need help with the interpretation.
ci mean income, level(95)
Variable | Obs Mean Std. Err. [95% Conf. Interval]
-------------+---------------------------------------------------------------
income | 3,544 59399.39 809.8514 57811.57 60987.21
ci mean income, level(99)
Variable | Obs Mean Std. Err. [99% Conf. Interval]
-------------+---------------------------------------------------------------
income | 3,544 59399.39 809.8514 57312.22 61486.55
Explanation / Answer
Given : x = 59399.39, SE = 809.8514 , n = 3544
For the 95% CI, = 0.05
The Zcritical (2 tail) for = 0.05, is 1.96
The Confidence Interval is given by x ± ME, where
ME = Zcritical * SE = 1.96 * 809.8514 = 1587.31
The Lower Limit = 59399.39 - 1587.31 = 57812.08
The Upper Limit = 59399.39 + 1587.31 = 60986.70
The interpretation is that we are 95% confident that the population mean lies in this interval.
For the 99% CI, = 0.01
The Zcritical (2 tail) for = 0.01, is 2.576
The Confidence Interval is given by x ± ME, where
ME = Zcritical * SE = 2.576 * 809.8514 = 2086.18
The Lower Limit = 59399.39 - 2086.18 = 57313.21
The Upper Limit = 59399.39 + 1587.31 = 61485.57
The interpretation is that we are 99% confident that the population mean lies in this interval.