Question

1. A survey of 30 emergency room patients found that the average waiting time for treatment was 174.3 minutes. Assuming that the population standard deviation is 46.5 minutes, find the best point estimate of the population mean. Construct and interpret the 99% confidence interval of the population mean.

Answer 1

Best point estimate for population mean is = 174.3

Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.01 /2) = 2.576
174.3 ± Z (0.01/2 ) * 46.5/√(30)
Lower Limit = 174.3 - Z(0.01/2) 46.5/√(30)
Lower Limit = 152.43
Upper Limit = 174.3 + Z(0.01/2) 46.5/√(30)
Upper Limit = 196.17
99% Confidence interval is ( 152.43 , 196.17 )

Interpretation = We are 99% confident that the true average waiting time for treatment is

between 152.43 min and 196.17 min