An experiment involves selecting a random sample of 256 middle managers for study. One item of interest is annual income. The sample mean is computed to be $35,420 and the sample standard deviation is $2,050. Using this information, calculate the 95% confidence interval (rounded to the nearest $10). Interpret your findings.
n = 256, = $35,420, and s = $2,050
Since sample size is quite large (n = 256 >> 30), therefore, using z-distribution.
For a 95 percent confidence interval, z = 1.960
95% confidence interval =
= = = ($35,170, $35,670)
The 95 percent confidence interval for the true mean annual income of middle managers is $35,170< ? < $35,670. An interval constructed this way has a probability of 0.95 of containing the true mean annual income of middle managers, ? (Doane & Seward, 2007).