Problem 1 (2 points) There has been an increasing amount of attention on supplementing America's power grids with solar panels and wind turbines to provide sources of renewable energy. However, unlike traditional sources that are weather-resistant, solar panels can only generate power while the sun is out, and wind turbines require enough windy weather. Hence, energy experts have called on companies to create many solar panels and wind turbines scattered across various parts of the power grid to counter this issue. In about 6 sentences, explain how the law of large numbers can be applied to here to explain why it is beneficial from an energy generation standpoint to hook up thousands of solar panels and wind turbines scatter across different places to the electric power grid vs. only a few of these in limited locations. (Hint: think about the reasoning behind the casino and insurance examples to get started). Problem 2 This problem uses the Job training.xlsx data posted on Canvas and requires Excel's Data Analysis Toolpak. Note that you must copy the output when asked for, but if it's not asked for then no output is required and you can just write the answer. A local job training program has been funded by the state of Virginia. You are contracted to evaluate the effectiveness of this program and determine if it has improved the hourly wages of workers. You have information on 600 people who applied to be part of the 12-week job training program. Due to capacity constraints, 200 of these applicants were accepted into the program while 400 were denied acceptance. The data includes hourly wages of all 600 individuals 1 year after the job training program ended, including those who were accepted into the job training program (Accepted) and those who were denied entry (Denied). For clarity, this is a cross-section of data after any job training has taken place. You want to compare the mean hourly wage of those who completed the job training vs. those who applied but were denied.

A. (2 points) Construct the 90% confidence interval and the 99% confidence interval for the mean hourly wage of those accepted into the program. Explain what these confidence intervals tell us and why there is a difference between these intervals. B. (1 point) Assuming a two-tailed test, what are the null hypothesis and alternative hypothesis of this study? C. (1 point) Use Excel's Data Analysis Toolpak to conduct the appropriate t-test for this study and copy and paste the output below. Hint: The unequal size of the samples is not a problem when conducting t-tests. D. (3 points) Based on a two-tailed test, determine if your results are statistically significant at the = 0.05 level and whether we reject the null hypothesis. Then do the same at the = 0.01 level. Explain how you arrived at these conclusions and be clear with your language. E. (1 point) T-tests assume that we have drawn the sample at random to make claims about the population. Based on the details of the job training program in the setup of the problem, describe whether we are working with random samples in this situation and why this is or is not a problem for drawing conclusion about the effectiveness of the job training program. About 3-5 sentences is fine here.

Accepted	Denied
12.58	8.33
7.61	11.55
16.83	8.69
7.57	12.23
12.64	11.14
9.75	16.25
15.9	10.92
20.02	10.11
9.59	9.95
7.98	7.05
14.7	13.52
32.42	10.54
25.33	7.85
11.16	14.22
9.59	14.39
8.25	12.64
14.7	10.17
8.86	12.13
9.75	8.22
7.98	9.25
12.44	7.22
7.61	7.08
9.17	9.8
15.42	6.85
13.99	9.71
13.58	8.43
12.66	11.36
15.05	11.46
26.75	12.38
7.52	7.59
7.13	7.59
20.17	9.71
11.16	15.7
9.03	7.64
7.2	6.19
8.45	12.38
7.59	6.48
9.89	11.22
11.16	12.19
8.59	20.65
14.2	6.3
9.91	7.59
7.61	14.44
11.78	11.94
7.61	10.84
11.16	9.25
12.69	7.96
9.4	7.96
7.68	12.53
12.93	8.21
11.37	9.87
10.59	20.78
15.42	11.29
12.35	8.69
20.72	9.43
8.79	21.68
8.12	7.22
7.98	19.42
11.16	9.69
25.33	11.64
7.31	12.01
10.81	12.01
8.24	8.33
9.89	13.11
25.33	14.92
30.63	13.85
9.75	9.28
9.01	7.96
8.05	20.97
20.02	11.24
7.44	6.48
9.52	11.79
11.02	11.64
9.67	9.87
12.66	14.83
7.68	17.58
14.7	12.71
11.86	14.83
8.05	9.71
10.29	7.37
9.89	10.35
13.63	10.24
25.33	7.63
13.28	3.85
8.95	26.87
13.63	11.64
20.61	6.67
8.95	18.93
9.75	6.96
10.29	6.48
15.23	8.84
20.61	18.85
7.7	7.73
15.23	7.22
9.91	8.94
14.2	9.06
7.76	7.85
8.22	4.92
12.55	23.19
13.21	6.63
10.21	15.55
31.07	11.29
9.71	12.01
9.25	10.72
12.29	10.17
7.13	8.84
12.93	13.11
8.42	7.96
7.13	7.68
8.05	7.9
44.22	9.8
9.4	24.9
12.29	8.1
14.48	9.19
20.17	10.17
9.4	6.58
7.61	13.41
9.4	12.38
15.42	6.34
7.52	7.4
14.7	10.72
11.86	21.22
25.33	20.5
9.75	14.97
7.63	12.36
23.42	7.4
20.15	10.87
18.24	8.69
9.28	6.3
11.16	11.29
13.99	13.85
9.4	20.21
19.66	14.29
8.6	18.01
12.93	11.52
12.11	16.96
15.9	17.17
14.48	12.13
11.16	19.08
7.31	12.93
11.73	10.17
7.31	6.85
20.61	10.9
8.27	9.25
7.11	14.77
14.7	10.85
12.66	6.48
7.62	6.63
8.05	5.89
20.58	35.2
11.16	9.8
12.93	8.69
7.54	10.78
12.1	19.08
11.51	9.22
71.32	11.66
8.22	9.87
15.67	9.59
16.83	9.43
9.59	6.58
15.42	12.71
16.12	11.29
12.93	21.96
28.02	25.82
9.28	7.96
9.89	12.38
39.98	8.33
15.05	7.4
26.52	9.47
9.4	16.96
9.97	8.69
26.75	6.48
8.05	9.38
8.05	11.29
7.31	7.55
12.47	6.48
12.1	6.85
7.83	13.41
10.63	9.68
12.29	6.3
8.22	12.01
7.61	10.17
13.37	10.72
16.12	11.16
7.13	25.24
7.52	12.36
7.57	7.96
10.11	10.54
8.79	9.64
13.13	6.48
7.52	7.4
13.13	12.93
7.19	11.64
11.16	7.52
8.6	8.51
11.16	5.56
10.26	9.02
9.4	11.29
8.35	12.36
15.42	16.06
	7.52
	17.53
	25.24
	13.11
	9.25
	7.59
	16.39
	11.64
	10.39
	30.8
	10.59
	11.29
	7.22
	10.74
	7.04
	6.48
	9.25
	17.53
	8.61
	13.85
	6.85
	9.15
	39.64
	14.6
	10.68
	11.97
	9.8
	13.85
	8.75
	7.17
	23.26
	10.35
	6.48
	13.85
	16.4
	10.9
	12.75
	12.62
	7.17
	7.05
	14.03
	10.54
	7.92
	7.22
	8.73
	11.64
	21.22
	12.93
	8.33
	10.9
	10.17
	7.4
	10.15
	8.47
	7.66
	9.43
	12.11
	6.96
	6.51
	9.43
	10.9
	9.06
	27.59
	7.96
	10.43
	6.99
	19.54
	22.55
	7.22
	10.7
	22.12
	36.8
	10.13
	9.06
	24.61
	6.85
	10.78
	8.61
	5.77
	14.53
	8.94
	9.71
	6.3
	10.73
	10.67
	8.88
	12.47
	18.38
	8.88
	6.83
	6.19
	10.9
	11.17
	13.41
	8.51
	12.18
	22.69
	9.06
	12.87
	10.17
	9.67
	28.22
	7.14
	8.88
	8.94
	6.48
	6.85
	7.37
	10.17
	23.47
	7.17
	14.68
	8.69
	10.54
	14.12
	11.36
	12.45
	13.34
	20.85
	7.07
	9.8
	16.96
	11.64
	15.14
	17.66
	7.71
	7.81
	9.52
	12.36
	20.37
	8.69
	11.49
	13.85
	15.69
	10.17
	10.74
	9.43
	15.88
	5.75
	9.06
	10.94
	10.17
	11.8
	10.01
	11.64
	10.9
	9.25
	38.22
	8.45
	7.22
	10.44
	14.59
	7.96
	11.29
	15.32
	7.22
	7.4
	12.23
	8.14
	6.12
	16.8
	11.27
	22.12
	9.43
	8.55
	9.12
	7.05
	8.33
	12.36
	8.05
	11.38
	8.84
	12.43
	7.33
	9.87
	21.49
	10.9
	8.33
	10.17
	15.9
	6.96
	7.22
	7.59
	10.17
	7.96
	11.64
	11.64
	9.23
	7.59
	12.5
	9.25
	7.59
	10.51
	9.5
	19.17
	10.59
	10.35
	7.96
	25.82
	9.43

One sample

Ounces 11.78284076 11.87098913 11.97785373 11.7837452 11.60367027 12.16583893 11.75968505 11.66778816 11.77515603 11.83696845 11.81201592 11.66539642 11.66658223 11.79564457 11.8558473 11.71323974 11.64732395 12.07723015 11.7233413 11.82576703 12.17918201 12.04388529 11.62997074 11.85752798 12.04302424 11.52787287 11.66604014 11.85599317 11.77106432 11.45720835

Two Sample

Method A Method B 72.47171449 72.14533547 72.10054831 89.81136212 69.70021876 98.07199674 61.29469083 84.48697781 76.50973633 80.53073819 81.2886421 84.8586 75.89828709 70.82839411 71.61030277 90.86379516 82.00560778 73.11393335 52.74303075 93.71550056 64.72014163 83.39992772 89.80799922 86.02511572 74.101 92.19116933 60.05217322 91.87672751 68.25017959 79.21653421

Paired

SubjectID Pretest Posttest 1 90.56294638 110.6419831 2 94.8157883 101.5879712 3 109.5622995 120.6071699 4 90.2216652 83.22167741 5 97.59779121 109.2724394 6 91.16687001 115.8063292 7 96.64991726 99.89580602 8 97.61625775 117.9404066 9 88.84491009 106.052309 10 90.8170057 82.82287975 11 89.29368686 116.6392647 12 115.8319456 128.6097677 13 121.2872833 119.6646412 14 87.87178703 108.3829938 15 93.79326196 96.37378628