Question

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.)

Answer 1

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)