Question 463873
H[o]:m=f
H[a]:m<>f
.
Let's do a 2 tailed test with a 95% confidence interval.
We will compare the means of the two samples.
M: x[m]=76, s=8, n=36
F: x[f]=80, s=6, n=36
.
{{{sigma(x[m]-x[f])=sqrt((sigma^2[m]/n[m])+(sigma^2[f]/n[f]))=sqrt((64/36)+(36/36))=1.67}}}
.
z=(76-80)/1.67=-2.40
Since -2.40 falls in the rejection area to the left of -1.96 then the H[o] is rejected and women are smarter than men.
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Ed