Question

The US Poultry & Egg association claims that eating 2 eggs every morning for breakfast will increase (i.e. improve) your High-density lipoprotein (HDL) cholesterol levels. To test their claim, you conduct an experiment on 10 randomly chosen subjects. For 12 weeks they eat 2 eggs for breakfast every morning, after which you measure their HDL level. Then they eat just toast for breakfast every morning for 12 weeks after which you measure their HDL level. The results are in the table below. Based on this data, is there evidence that eggs increase your HDL level? Use a = 0.05.

Subject 1 2 3 4 5 6 7 8 9 10

HDL after eggs 60 63 70 75 55 50 62 56 71 48

HDL after toast 61 60 65 75 62 53 55 55 62 50

Answer 1

let d =after-Before

null Hypothesis:μd		=	0
alternate Hypothesis: μd		>	0

0.05 level with right tail test and n-1= 9 df, critical t=			1.833	from excel: 1*t.inv(0.05,9)
Decision rule: reject Ho if test statistic t>1.833

S. No	after	Before	diff:(d)=x1-x2	d2
1	60	61	-1	1.00
2	63	60	3	9.00
3	70	65	5	25.00
4	75	75	0	0.00
5	55	62	-7	49.00
6	50	53	-3	9.00
7	62	55	7	49.00
8	56	55	1	1.00
9	71	62	9	81.00
10	48	50	-2	4.00
	total	=	Σd=12	Σd2=228
	mean dbar=	d̅     =	1.2000
	degree of freedom =n-1                            =		9
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		4.871687
	std error=Se=SD/√n=		1.5406
	test statistic            =	(d̅-μd)/Se         =	0.7789
	p value	=	0.2280	from excel: tdist(0.779,9,1)

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that eggs increase your HDL level