Question

(1 point) A random sample of n measurements was selected from a population with unknown mean y and standard deviation o. Calculate a 95% confidence interval for u for each of the following situations: (a) n = 100, X = 35.1, s = 3.61 sus (b) n= 110, x = 53.2, s = 3.36 Sus .. (c) n = 115, x = 68.3, s = 4.76 18 SMS !!! (d) n=95, x = 41, s = 2.81 !!! Sus

Answer 1

part a)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 100- 1 ) = 1.984
35.1 ± t(0.05/2, 100 -1) * 3.61/√(100)
Lower Limit = 35.1 - t(0.05/2, 100 -1) 3.61/√(100)
Lower Limit = 34.392
Upper Limit = 35.1 + t(0.05/2, 100 -1) 3.61/√(100)
Upper Limit = 35.808
95% Confidence interval is ( 34.392 , 35.808 )

Part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 110- 1 ) = 1.982
53.2 ± t(0.05/2, 110 -1) * 3.36/√(110)
Lower Limit = 53.2 - t(0.05/2, 110 -1) 3.36/√(110)
Lower Limit = 52.572
Upper Limit = 53.2 + t(0.05/2, 110 -1) 3.36/√(110)
Upper Limit = 53.828
95% Confidence interval is ( 52.572  , 53.828 )

Part c)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 115- 1 ) = 1.981
68.3 ± t(0.05/2, 115 -1) * 4.76/√(115)
Lower Limit = 68.3 - t(0.05/2, 115 -1) 4.76/√(115)
Lower Limit = 67.430
Upper Limit = 68.3 + t(0.05/2, 115 -1) 4.76/√(115)
Upper Limit = 69.170
95% Confidence interval is ( 67.430 , 69.170 )

Part d)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 95- 1 ) = 1.986
41 ± t(0.05/2, 95 -1) * 2.81/√(95)
Lower Limit = 41 - t(0.05/2, 95 -1) 2.81/√(95)
Lower Limit = 40.435
Upper Limit = 41 + t(0.05/2, 95 -1) 2.81/√(95)
Upper Limit = 41.565
95% Confidence interval is ( 40.435 , 41.565 )