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# Statistics - Inference about population mean

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Comparing two drugs. Makers of generic drugs must show that the do not differ significantly from the "reference" drugs that they imitate. One aspect in which drugs might differ is their extent of absorption in the blood. Table gives data taken from 20 healthy nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Numbers 1 to 20 were assigned at random to the subjects. Subjects I to 10 received the generic drug first, and Subjects 11 to 20 received the reference drug first. In all cases, a washout period separated the two drugs so that the first had disappeared from the blood before the subject took the second. Do the drugs differ significantly in absorption?

Table Absorption extent for two versions of a drug.

SUBJECT REFERENCE DRUG GENERIC DRUG
15 4108 1755
3 2526 1138
9 2779 1613
13 3852 2254
12 1833 1310
8 2463 2120
18 2059 1851
20 1709 1878
17 1829 1682
2 2594 2613
4 2344 2738
16 1864 2302
6 1022 1284
10 2256 3052
5 938 1287
7 1339 1930
14 1262 1964
11 1438 2549
1 1735 3340
19 1020 3050

Checking understanding of application.

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## Statistics - Inference about a population mean

The placebo effect. The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, scientists measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is given. The same six patients are measured both with and without the placebo, at different times.

(a) Explain why the proper procedure to compare the mean response to placebo with control (no treatment) is a matched pairs t test.

(b) The six differences (treatment minus control) had the mean = -0.326 and s = 0.181. Is there significant evidence of a difference between treatment and control?

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