Based on the following scores can you test whether there are

Based on the following scores, can you test whether there are gender-associated differences in mathematical skills at alpha = 0.05 ?

Boys : <80 96 98 87 75 83 70 92 97 82>

Girls : <82 90 84 70 80 97 76 90 88 86>

Group the grades into the intervals : [70, 75), [75, 80), [80, 85), [85, 90), [90, 100)

Boys : <80 ,96, 98, 87, 75, 83, 70, 92, 97, 82>

Mean X1 = 86

n1 = 10

SD1 = 9.66

Girls : <82, 90, 84, 70, 80, 97, 76, 90, 88, 86>

Mean X2 = 84.3

n2 = 10

SD2 = 7.75

z = ( X1 -X2)/ sqrt((SD1^2/n1 + SD2^2/n2)

= ( 86 -84.3)/ sqrt((9.66)^2/10 + (7.75)^2/10)

= 0.43

Two tailed test :

P value = 2(1-0.6664) = 0.6672

P>0.05 Therefore , yes there are gender assiciated differences .