Question

It is well documented that cholesterol over 200 is a risk factor in developing heart disease for both men and women (www.livestronge.com, January 11, 2011). Younger men are known to have higher cholesterol levels than younger women; however, beyond the age of 55, women are more likely to have higher cholesterol levels. a recent college graduate working at a local blood lab has access to the cholesterol data of 50 men and 50 women in the 20 - 40 age group. the accompanying table shows a portion of the data.

Men	Women
181	178
199	193
189	185
187	188
205	190
188	193
192	190
186	195
196	201
196	191
191	182
194	205
200	184
209	190
194	186
197	182
188	199
219	188
194	202
195	177
194	197
194	178
192	184
190	189
189	183
198	180
193	197
191	195
195	195
202	198
188	199
207	185
180	180
188	187
198	179
204	198
204	189
203	198
213	192
187	172
193	197
189	192
196	173
199	194
198	205
182	197
199	174
174	185
194	171
190	182

At the 1% significance level, determine if there are any differences in the mean cholesterol levels for men and women in the age group. It is fair to assume that the population variance for men and women are equal?

*please show all work*

Answer 1

X : cholesterol level for Men

Y: cholesterol level for Women

	X	Y	(X-X̅)	(X-X̅)2	Y-Y̅	(Y-Y̅)2
	181	178	-13.48	181.7104	-10.88	118.3744
	199	193	4.52	20.4304	4.12	16.9744
	189	185	-5.48	30.0304	-3.88	15.0544
	187	188	-7.48	55.9504	-0.88	0.7744
	205	190	10.52	110.6704	1.12	1.2544
	188	193	-6.48	41.9904	4.12	16.9744
	192	190	-2.48	6.1504	1.12	1.2544
	186	195	-8.48	71.9104	6.12	37.4544
	196	201	1.52	2.3104	12.12	146.8944
	196	191	1.52	2.3104	2.12	4.4944
	191	182	-3.48	12.1104	-6.88	47.3344
	194	205	-0.48	0.2304	16.12	259.8544
	200	184	5.52	30.4704	-4.88	23.8144
	209	190	14.52	210.8304	1.12	1.2544
	194	186	-0.48	0.2304	-2.88	8.2944
	197	182	2.52	6.3504	-6.88	47.3344
	188	199	-6.48	41.9904	10.12	102.4144
	219	188	24.52	601.2304	-0.88	0.7744
	194	202	-0.48	0.2304	13.12	172.1344
	195	177	0.52	0.2704	-11.88	141.1344
	194	197	-0.48	0.2304	8.12	65.9344
	194	178	-0.48	0.2304	-10.88	118.3744
	192	184	-2.48	6.1504	-4.88	23.8144
	190	189	-4.48	20.0704	0.12	0.0144
	189	183	-5.48	30.0304	-5.88	34.5744
	198	180	3.52	12.3904	-8.88	78.8544
	193	197	-1.48	2.1904	8.12	65.9344
	191	195	-3.48	12.1104	6.12	37.4544
	195	195	0.52	0.2704	6.12	37.4544
	202	198	7.52	56.5504	9.12	83.1744
	188	199	-6.48	41.9904	10.12	102.4144
	207	185	12.52	156.7504	-3.88	15.0544
	180	180	-14.48	209.6704	-8.88	78.8544
	188	187	-6.48	41.9904	-1.88	3.5344
	198	179	3.52	12.3904	-9.88	97.6144
	204	198	9.52	90.6304	9.12	83.1744
	204	189	9.52	90.6304	0.12	0.0144
	203	198	8.52	72.5904	9.12	83.1744
	213	192	18.52	342.9904	3.12	9.7344
	187	172	-7.48	55.9504	-16.88	284.9344
	193	197	-1.48	2.1904	8.12	65.9344
	189	192	-5.48	30.0304	3.12	9.7344
	196	173	1.52	2.3104	-15.88	252.1744
	199	194	4.52	20.4304	5.12	26.2144
	198	205	3.52	12.3904	16.12	259.8544
	182	197	-12.48	155.7504	8.12	65.9344
	199	174	4.52	20.4304	-14.88	221.4144
	174	185	-20.48	419.4304	-3.88	15.0544
	194	171	-0.48	0.2304	-17.88	319.6944
	190	182	-4.48	20.0704	-6.88	47.3344
Total	9724	9444		3366.48		3751.28
Mean	X̅	Y̅
	194.48	188.88