Answer to Question #94394 in Statistics and Probability for TRACY HAWKINS

Question

If a sample of 50 grades from a statistics test has a mean of 81.6 & gives a sample standard deviation of 8.3, what is the 95% comfidence interval for the population mean?

Answer 1

Confidence Interval for the Mean (CI) = mean (m) ± margin of error (ME)

m = 81.6

$ME=Z*S/\sqrt{n}$

n = 50; S = 8.3; Z_95% = 1.96

$ME=1.96*8.3/\sqrt{50}$

$ME=2.30$  

95% CI for the Mean = 81.6 ± 2.30 = (79.3, 83.9)

The 95 percent confidence interval for the mean ranges between 79.3 and 83.9