1. The company Drug Test Success provides a "1-Panel-THC" test for marijuana usage. In a simple random sample of 300 tested subjects, results from 27 were wrong (either a false positive or a false negative).

a) Find the proportion of "1-Panel-THC" test results in this sample that are wrong. SHOW ALL THE NECESSARY WORK.

b) Use a 0.05 level of significance to test the claim that less than 10% of the test results are wrong. Assume that all the requirements for testing a claim about the proportion of the population are satisfied (so no need to mention them!!). SHOW ALL THE NECESSARY WORK. Don't forget to state your conclusion. IF YOU USE THE P-VALUE METHOD, please show me THE EXCEL COMMANDS TO DETERMINE THE P-VALUE. (Show everything in excel command)

1. Research scientists at a pharmaceutical company have recently developed a new nonprescription sleeping pill. They decide to test its effectiveness by measuring the time it takes for people to fall asleep after taking the pill. Preliminary analysis indicates that the time to fall asleep varies considerably from one person to another. Consequently, they organize the experiment in the following way. A random sample of 100 volunteers who regularly suffer from insomnia is chosen. Each person is given one pill containing the newly developed drug and one placebo. (They do not know whether the pill they are taking is the placebo or the real thing, and the order of use is random.) Each participant is fitted with a device that measures the time until sleep occurs.

Drug	Placebo
19	20
12	18
20	29
18	20
24	33
20	30
25	34
26	26
23	19
25	29
17	22
13	14
16	18
20	32
13	8
26	28
19	23
22	19
12	18
17	22
20	30
20	17
29	29
12	23
20	17
19	6
15	15
25	39
19	17
27	32
18	22
33	28
14	9
13	10
26	34
21	20
20	23
23	28
20	32
19	29
22	21
14	14
20	14
20	32
21	33
25	34
17	21
11	9
10	5
23	39
12	19
11	12
19	15
18	15
23	25
17	30
15	15
20	19
23	22
15	20
24	38
21	32
5	9
22	22
15	7
16	22
23	16
22	31
8	15
13	21
16	23
9	14
13	22
23	33
25	25
29	26
11	15
19	31
24	32
15	21
16	23
19	12
23	31
23	21
15	22
13	11
14	13
10	8
21	21
10	11
18	20
15	21
4	11
23	30
26	33
25	27
8	17
16	30
19	24
16	26

Use a 0.01 level of significance to test the claim that the new drug is effective. Assume that all the requirements for testing a claim about the differences in matched pairs are satisfied (so no need to mention them!!). SHOW ALL THE NECESSARY WORK. Don't forget to state your conclusion. IF YOU USE THE P-VALUE METHOD, YOU HAVE TO USE THE EXCEL COMMANDS TO DETERMINE THE P-VALUE. (Show everything with excel command please)