Question

The population standard deviation (σ) for a standardized achievement test that is normally distributed is 8.  
 a.) Calculate the standard error of the mean if you draw a random sample of 50 test scores.  Show your work for full credit .  .  .
 b.) Your sample mean is calculated to be 77.  Compute the 95% confidence interval for the mean.  Show your work!
 c.) Interpret the meaning of the 95% confidence interval in one sentence.

Answer 1

Here are a few hints to get you started:

a). Standard error of the mean = standard deviation divided by the square root of the sample size

b). CI95 = mean ± 1.96(sd/√n)
...where ± 1.96 represents the 95% interval using a z-table, sd = standard deviation, and n = sample size

c). You are 95% confident that the population mean is within the interval.