Construct a 90% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug. Let Population 1 be the initial cholesterol level and Population 2 be the cholesterol level after three months. Round the endpoints of the interval to one decimal place, if necessary.
A pharmaceutical company is running tests to see how well its new drug lowers cholesterol. Twelve adults volunteer to participate in the study. The total cholesterol level of each participant (in mg/dL) is recorded once at the start of the study and then again after three months of taking the drug. The results are given in the following table. Construct a 90% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug. Let Population 1 be the initial cholesterol level and Population 2 be the cholesterol level after three months. Round the endpoints of the interval to one decimal place, if necessary.
Total Cholesterol Levels (in mg/dL)
| Initial Level | Level after Three Months |
|---|---|
| 196 | 189 |
| 190 | 195 |
| 190 | 197 |
| 212 | 192 |
| 218 | 197 |
| 211 | 219 |
| 230 | 197 |
| 191 | 182 |
| 202 | 202 |
| 202 | 187 |
| 216 | 190 |
| 227 | 213 |
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