Question

Construct the indicated confidence interval for the population mean using​ (a) a​ t-distribution. (b) If you had incorrectly used a normal​ distribution, which interval would be​ wider? C equals 0.95, x overbar equals14.6, S equals 4.0, n equals 5.

​(Round to one decimal place as​ needed.)

Answer 1

Confidence interval for t distribution:

x̅ = 14.6, s = 4, n = 5  

95% Confidence interval :  

At α = 0.05 and df = n-1 = 4, two tailed critical value, t-crit = T.INV.2T(0.05, 4) =    2.776

Lower Bound = x̅ - t-crit*s/√n = 14.6 - 2.776 * 4/√5 = 9.6

Upper Bound = x̅ + t-crit*s/√n = 14.6 + 2.776 * 4/√5 = 19.6

9.6 < µ < 19.6