x bar is 17.
stadnard deviation of the mean is 4/sqrt(3) = 2.31
z score = (17 - 15)/2.31 = .866
p value = .36, do not reject with alpha of .05
Do the same problem, but now sigma is unknown.
variance = 4
s = 2
standard error of the mean = 2/(sqrt(3) = 1.15
t(2) = (17 - 15)/1.15 = 1.74
p value = .22, do not reject with alpha of .05
Another researcher wants to compare the effect on boys and girls. He gets a sample of three girls, 10, 15, 20, as well as a sample of boys, 14, 20, 26. Are boys and girls affected differently by the power lines?
x bar girls = 15
x bar boys = 20
variance for girls = 25
variance for boys = 36
pooled variance = (2*25+2*36)/4 = 30.5
pooled standard deviation = 5.52
t(4) = (15-20) / 5.52*sqrt(1/3 + 1/3) = -1.09
p value = .34, do not reject with alpha of .05