here as sample size is high we may use z distribution
male | female | ||||
x1 = | 28.000 | x2 = | 39.000 | ||
n1 = | 65.000 | n2 = | 65.000 | ||
σ1 = | 3.000 | σ2 = | 2.000 | ||
std error of difference σ1-σ2= | √(σ21/n1+σ22/n2) = | 0.4472 |
for 98 % CI value of z= | 2.3263 | ||||
margin of error E=z*std error = | 1.0404 | ||||
lower confidence bound=estimated mean diff.-margin of error = | -12.04 | ||||
Upper confidence bound=estimated mean diff+margin of error= | -9.96 |
hence 98% CI =-12.04<1-2 <-9.96
(Note from t - distributioon this interval can be (-12.06 ; -9.94) or (-12.05 ; -9.95)
A study of working actors looked at age and gender. One sample of 65 male actors...
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