smoke
	female	male			female	male		sigma of p1-p2
	yes	no		no	30	30		=SQRT(F9^2 +G9^2)	0.09858293
	no	no		yes	14	11
	no	yes		p	0.31818182	0.26829268
	yes	no		N	44	41
	no	yes		sigma_p	0.07021754	0.06919603		two tail cutoff
	no	no						=NORMINV(0.995, 0, 0.1)	0.25758313
	no	no
	no	no	Is there a difference in male / female smoking habits? The data from our suvey are shown at the left; the summary is above. (I used the =countif(range,text) Excel function to do the counting. Or you could sort the entries and subtract column numbers.) Procedure: difference of percentages. p1 = fraction of males who smoke p2 = fraction of females who smoke H0: the percentage of smokers is the same for males and females. p1 = p2 Halpha: the percentages are different. (two tail) Standard deviation of percentage is sqrt(p*(1-p)/N) which gives sigma_p1 = 0.07521, sigma_p2 = 0.07526. Standard deviation of the difference is sqrt( s1^2 + s2^2 ) = 0.10 Choosing significance level alpha=0.01, our two-tail cutoff is given by NORMINV(0.995, 0, 0.10) = 0.26. In other words, a normal variable with mean=0 and sigma=0.1 is in the range (-0.26 < x < 0.26) 99% of the time. Our decision rule is to reject the null hypothesis if p1-p2 is >0.26 or p1-p2 is < -0.26. The result is that p1-p2 = 0.32 - 0.27 = 0.05, and we fail to reject the null hypothesis. Therefore from this data we can *not* conclude that there is a difference in the smoking habits of male and female Marlboro students. (At least, not at the 99% signficance level.) The confidence intervals give the same intuition; at 2sigma (95%), p1=0.32+-0.14; p2=0.27+-0.14. These ranges overlap, and so the two don't look all that different.
	no	yes
	yes	no
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