In: Statistics and Probability
15. Construct the indicated confidence interval for the population mean mu using the t-distribution. Assume the population is normally distributed. cequals0.98, x overbarequals13.8, sequals0.74, nequals19 left parenthesis nothing comma nothing right parenthesis (Round to one decimal place as needed.)
Given
c = 0.98 => we have to find 98% confidence
interval
X̅ = 13.8 Sample Mean
s = 0.74 Sample Standard
Deviation
n = 19 Sample Size
we have to find the confidence interval using
t-distribution
Confidence interval for population mean is given
by
Degrees of freedom = df = n - 1 = 19 - 1 =
18
For 98%, α = 0.02
From Excel function T.INV.2T(0.02, 18)
t = T.INV.2T(0.02, 18) =
2.55237963
= (13.4, 14.2)
Answer :
98% confidence interval is (13.4,
14.2)