Question

Do 9-year-old boys and girls have different average height? Please answer the question by performing an appropriate hypothesis test at the 10% significance level based on the sample results below:

Boys: n1= 60, 1x=123, S1= 10

Girls: n2= 50, 1x=126, S2= 1

Answer 1

since sample size for both is greater than 30; we can use large sample z distribution.

null hypothesis: Ho:μ1-μ2	=	0
Alternate hypothesis: Ha:μ1-μ2	≠	0
for 0.1 level with two tail test , critical z=		1.645
Decision rule : reject Ho if absolute value of test statistic |z|>1.645

	Boys		Girls
x1            =	123.00	x2            =	126.00
n1           =	60	n2           =	50
σ1           =	10.00	σ2           =	1.00

std error σx1-x2=√(σ21/n1+σ22/n2)    =sqrt(10^2/60+1^2/50) =

1.299

test statistic z =(x1-x2-Δo)/σx1-x2     =(123-126)/1.299 =

-2.31

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that 9-year-old boys and girls have different average height