Discuss the below:
The Hydronics Company is in the business of developing health supplements. Recently, the company's R&D department came up with two weight-loss plans that included products produced by Hydroniccs. To determine whether these products are effective, the company has conducted a test. A total of 300 people who each were 30 pounds or more overweight were recruited to participate in the study. Of these, 100 people were given a placebo supplement, 100 people were given plan 1, and 100 people were given plan 2. As might be expected, some people dropped out before the four-week study period was completed. The weight loss (or gain) for each individual is listed in the data file. Note positive values indicate that the individual actually gained weight during the study period.
a. Develop a frequency histogram for the weight loss (or gain) for those people on plan 1, does it appear from this graph that weight loss is approximately normally distributed?
b. Referring to part a, assuming that a normal distribution does apply, compute the mean and standard deviation weight loss for the plan 1 subjects.
c. Referring to part a and b, assuming that the weight change distribution for plan 1 users is normally distributed and that the sample mean and standard deviation are used to directly represent the population mean and standard deviation. Then, what is the probability that a plan 1 user will lose more than 12 pounds in a four-week period?
d. Referring to your answer in part c, would it be appropriate for the company to claim that plan 1 users can expect to lose as much as 12 pounds in four weeks? Discuss
| Subject |
Placebo |
Product # 1 |
Product # 2 |
| 1 |
-3.1 |
2.8 |
5.6 |
| 2 |
-7.9 |
1.2 |
5.5 |
| 3 |
-0.3 |
3.6 |
6.2 |
| 4 |
4.8 |
-15.5 |
9.1 |
| 5 |
4.4 |
-2.7 |
-2.3 |
| 6 |
7.1 |
0.2 |
4.3 |
| 7 |
-12.5 |
3.7 |
-1.9 |
| 8 |
-2.7 |
-5.9 |
5.1 |
| 9 |
3.9 |
-1 |
-6.6 |
| 10 |
-7 |
13.7 |
-3.9 |
| 11 |
-5 |
0.9 |
1.1 |
| 12 |
-10 |
8.4 |
3.7 |
| 13 |
-10.8 |
0.1 |
-1.9 |
| 14 |
-6.4 |
-2.9 |
5.5 |
| 15 |
-5.4 |
-1.4 |
15.7 |
| 16 |
-12.1 |
-2.5 |
5.4 |
| 17 |
-4.4 |
-0.2 |
-2 |
| 18 |
-3.6 |
6.7 |
7.3 |
| 19 |
-0.9 |
5.3 |
-2.9 |
| 20 |
-3.4 |
6.1 |
9.6 |
| 21 |
-3.2 |
-4.4 |
3.8 |
| 22 |
-3.4 |
2.6 |
2.8 |
| 23 |
5.2 |
2.3 |
-5.2 |
| 24 |
-2 |
-1.2 |
-0.9 |
| 25 |
-2.5 |
6.9 |
8.5 |
| 26 |
-4.1 |
0.1 |
-0.3 |
| 27 |
8.3 |
-0.4 |
5.3 |
| 28 |
2.8 |
2.3 |
-1.4 |
| 29 |
10.3 |
0.8 |
4.4 |
| 30 |
-4.8 |
-0.6 |
-0.1 |
| 31 |
6.8 |
-0.8 |
6.1 |
| 32 |
-9.6 |
-4.3 |
6.9 |
| 33 |
1.1 |
7.2 |
5.7 |
| 34 |
3 |
7.6 |
-2.4 |
| 35 |
8 |
4.9 |
3.3 |
| 36 |
-2 |
5.9 |
8.6 |
| 37 |
-4.2 |
5.2 |
-2.4 |
| 38 |
1.8 |
1.5 |
3.8 |
| 39 |
-3.5 |
8.5 |
-1.9 |
| 40 |
2.2 |
8.5 |
10.5 |
| 41 |
-8.8 |
4.9 |
10.3 |
| 42 |
-5.8 |
10.4 |
3.2 |
| 43 |
-9.2 |
6.7 |
0.6 |
| 44 |
-3.4 |
-2.5 |
5.7 |
| 45 |
-1.7 |
9.2 |
-0.7 |
| 46 |
-1.4 |
5.7 |
-0.4 |
| 47 |
-3.2 |
-0.5 |
-2.2 |
| 48 |
9.4 |
10.8 |
11.1 |
| 49 |
-10.3 |
0.2 |
9.5 |
| 50 |
-5.2 |
5.3 |
8.9 |
| 51 |
-14.4 |
2.6 |
3.8 |
| 52 |
5.7 |
0 |
-3.1 |
| 53 |
-7.9 |
2.9 |
-2.5 |
| 54 |
-4.8 |
1.2 |
-4.8 |
| 55 |
2.2 |
4 |
3.1 |
| 56 |
0.8 |
4.8 |
0.1 |
| 57 |
2.8 |
3.6 |
-0.2 |
| 58 |
1.4 |
5.6 |
-1.7 |
| 59 |
-8.4 |
7.3 |
2.3 |
| 60 |
-7.1 |
-0.2 |
3.6 |
| 61 |
1.9 |
8.5 |
-5 |
| 62 |
0.1 |
8.8 |
6.1 |
| 63 |
-6.2 |
-1.2 |
2.3 |
| 64 |
-2.8 |
6.5 |
4.8 |
| 65 |
-0.9 |
8 |
7.7 |
| 66 |
1.2 |
-7.6 |
-1.3 |
| 67 |
-0.9 |
-0.3 |
5.1 |
| 68 |
-6.1 |
5.1 |
-1.8 |
| 69 |
7.9 |
5.9 |
-1.2 |
| 70 |
0.9 |
4 |
-2.4 |
| 71 |
-1.2 |
0.5 |
9.9 |
| 72 |
2.6 |
-2.2 |
1.9 |
| 73 |
2.8 |
3 |
3.4 |
| 74 |
-4.7 |
-7.6 |
-4.6 |
| 75 |
-6.2 |
5.1 |
2.4 |
| 76 |
4 |
0.8 |
2.1 |
| 77 |
-7.6 |
-6.9 |
-1.9 |
| 78 |
-9.3 |
0.9 |
1.7 |
| 79 |
2 |
7.6 |
-2.7 |
| 80 |
1.6 |
1.5 |
-3.4 |
| 81 |
9.5 |
0.1 |
17.1 |
| 82 |
5.7 |
1.7 |
2.3 |
| 83 |
5 |
6.7 |
7.7 |
| 84 |
-1 |
-6.7 |
|
| 85 |
-1.5 |
6.8 |
|
| 86 |
0.7 |
-1.4 |
|
| 87 |
-1.7 |
4.5 |
|
| 88 |
-6.8 |
0.9 |
|
| 89 |
-10.4 |
3.5 |
|
| 90 |
|
3.5 |
|
| 91 |
|
8 |
|