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*
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 |
It is well documented that cholesterol over 200 is a risk factor in developing heart disease...
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