Question

If n = 16, ¯xx¯ = 30, and s = 7, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

< μμ <

Answer 1

As sample size is small (n=16) and population standard deviation is not given , also data comes from normal population , we use t distribution to find the confidence interval for mean

The 80% confidence interval for mean is

degrees of freedom = n-1 = 16-1=15

For 80% confidence ( =0.20) with df =15 , critical value of t is

tc =1.341 (from t table)

Thus, 80% confidence interval for mean is

= (27.653 , 32.347 )

Answer is : 27.653 < < 32.347