a. Construct a 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months. For credit, your work must include a filled out formula for your confidence interval.b. After the study was completed, the pharmaceutical company claims that the cholesterol levels have decreased. Does this confidence interval contradict this claim? Explain why. 14. A pharmaceutical company is testing a new drug that is supposed to lower cholesterol levels. Ten volunteersparticipate in a 3 month study that compares their cholesterol level before and after the 3 month treatment. Theresults are below. Units of measure are mg/dL.Initial Level210 200 215 194 206 221 203 189 208 211Level after 3 months 201 195 208 197 200 203 190 188 210 210

(a) The objective is to construct a 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months. The formula to compute the confidence interval is: C.I=d¯±t*sdn where, d¯ is the mean of the differences sd is the standard deviation of the differences t* is the t critical value. Required calculations: Before After d=After-Before 210 201 -9 200 195 -5 215 208 -7 194 197 3 206 200 -6 221 203 -18 203 190 -13 189 188 -1 208 210 2 211 210 -1 ∑di=-55 Mean of the differences is: d¯=∑din=-5510=-5.5 Standard deviation of the differences is computed as follows: sd=∑di-d¯2n-1=-9-(-5.5)2+-5-(-5.5)2+-7-(-5.5)2+.....+-1-(-5.5)210-1=6.637436 Using the t-table, t critical value at degrees of freedom df=10-1=9 and 95% confidence level is: 2.262 Substitute the values in the formula: C.I=d¯±t*sdn=-5.5±2.2626.63743610=-5.5±4.747805805=-5.5-4.747805805, -5.5+4.747805805≈-10.25, -0.75 Thus, the 95% confidence interval for the true mean decrease in cholesterol levels for people who take the drug treatment for 3 months is (-10.25, -0.75). (b) Given that, after the study was completed, the pharmaceutical company claims that the cholesterol levels have decreased. The confidence interval obtained in part (a) does not contradict this claim, because the confidence interval includes only negative values (does not include zero). Thus, it can be concluded that there is a true mean decrease in cholesterol levels for people who take the drug treatment for 3 months (i.e., After group).