Question

A researcher performed a retrospective study of the records of patients receiving care for hypercholesterolemia. The data gives measurements of total cholesterol for patients before and 6 weeks after taking a statin drug. Is there sufficient evidence at the α=.05 level significance to conclude that on an average the drug would result in reduction in total cholesterol in hypercholesterolemia patients. Assume total cholesterol in hypercholesterolemia patients is normally distributed

Using a Paired Sample t-test, what is the critical value of the test statistic?

Subject	Before Taking Statin Drug	After taking Statin Drug
1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 41.00 42.00 43.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 59.00 60.00 61.00 62.00 63.00 64.00 65.00 66.00 67.00 68.00 69.00 70.00 71.00 72.00 73.00 74.00 75.00 76.00 77.00 78.00 79.00 80.00 81.00 82.00 83.00 84.00 85.00 86.00 87.00 88.00 89.00 90.00 91.00 92.00 93.00 94.00 95.00 96.00 97.00 98.00 99.00 100.00 101.00 102.00 103.00 104.00 105.00 106.00 107.00	195.00 208.00 254.00 226.00 290.00 239.00 216.00 286.00 243.00 217.00 245.00 257.00 199.00 277.00 249.00 197.00 279.00 226.00 262.00 231.00 234.00 170.00 242.00 186.00 223.00 220.00 277.00 235.00 216.00 197.00 253.00 209.00 245.00 217.00 187.00 265.00 221.00 245.00 250.00 266.00 240.00 218.00 278.00 185.00 280.00 278.00 223.00 205.00 285.00 314.00 235.00 248.00 291.00 231.00 208.00 263.00 205.00 230.00 250.00 209.00 269.00 261.00 255.00 275.00 239.00 298.00 265.00 220.00 196.00 177.00 211.00 244.00 205.00 298.00 305.00 262.00 320.00 271.00 195.00 345.00 223.00 220.00 279.00 252.00 246.00 304.00 292.00 276.00 250.00 236.00 256.00 269.00 235.00 184.00 253.00 352.00 266.00 321.00 233.00 224.00 274.00 222.00 194.00 293.00 262.00 306.00 239.00	125.00 164.00 152.00 144.00 212.00 171.00 164.00 200.00 190.00 130.00 170.00 182.00 153.00 204.00 174.00 160.00 205.00 159.00 170.00 180.00 161.00 139.00 159.00 114.00 134.00 166.00 170.00 136.00 134.00 138.00 181.00 147.00 164.00 159.00 139.00 171.00 191.00 164.00 162.00 180.00 161.00 168.00 200.00 139.00 207.00 200.00 134.00 133.00 161.00 203.00 152.00 198.00 193.00 158.00 148.00 203.00 156.00 161.00 150.00 181.00 186.00 164.00 164.00 195.00 169.00 177.00 217.00 191.00 129.00 142.00 138.00 166.00 151.00 163.00 171.00 129.00 191.00 167.00 158.00 192.00 117.00 114.00 181.00 167.00 158.00 190.00 177.00 148.00 169.00 185.00 172.00 188.00 172.00 151.00 156.00 219.00 186.00 206.00 173.00 109.00 109.00 136.00 131.00 228.00 211.00 192.00 174.00

Answer 1

Let us denote the difference

d = total cholesterol before - total cholesterol after

There is sufficient evidence to conclude that on an average the drug would result in reduction in total cholesterol in hypercholesterolemia patients.