University of Iowa Excel Statistics Worksheet

Responses of fans:24
32
28
24
23
19
47
27
29
30
18
14
18
26
21
8
44
13
21
19
18
35
24
12
38
33
33
20
33
27
42
31
30
31
23
26
28
35
18
38
31
26
27
34
1)
(6 pts in total, parts a through e, scroll down to see all parts)
Suppose you are a sports columnist for your local basketball team. The star player, Du
there is so much that the fans expect of him that it seems like it’s never enough, and t
fan what he or she thought was the number of points scored by Dunkin’ Joe in last nig
You decide to perform a hypothesis test to test your suspicion and you collect sample
by Dunkin’ Joe in last night’s game. The 50 responses are shown to the left, in column
a) (1 pt) State the relevant null and alternative hypotheses that are of interest in this
which represents the true population mean of all the fans’ responses (if they w
H0 (null):
H1 (alternative):
b) (1 pt) Based upon the sample data in column A, what is the value of the test statis
c) (1 pt) What is the p-value? (Show work/code Excel formula)
d) (2 pts) Construct the appropriate confidence interval to test the hypothesis, assum
a 2% chance of a Type I error. (Show work/provide justification/code Excel fo
Lower bound:
Upper bound:
e) (1 pt) Still assuming an alpha of .02, which hypothesis do you favor? Highlight yo
Accept the null
Reject the null
29
24
52
30
29
26
tball team. The star player, Dunkin’ Joe, scored 30 points in last night’s game, and while this is a terrifically high number,
ms like it’s never enough, and the star player appears to be under-appreciated. You suspect that if you were to ask every
cored by Dunkin’ Joe in last night’s game, the average of their responses would be less than 30.
spicion and you collect sample data by asking 50 randomly selected fans how many points he or she thinks were scored
re shown to the left, in column A.
heses that are of interest in this situation. [Hint: The hypothesis test concerns µ (which you can write as µ or mu),
all the fans’ responses (if they were all surveyed) regarding the number of points they think Dunkin’ Joe scored in last night’s ga
at is the value of the test statistic? (Show work/code Excel formula)
val to test the hypothesis, assuming that you’re comfortable with an alpha of .02, that is you are comfortable with
ovide justification/code Excel formula/etc.)
sis do you favor? Highlight your answer and provide a brief justification.
Justification:
kin’ Joe scored in last night’s game.]
Sales
Advertising Highly paid
12.17
4.41
NO
9.98
5.61
NO
24.29
9.35
YES
35.81
11.71
NO
21.36
8.30
NO
28.01
9.66
NO
35.44
9.62
NO
18.07
7.84
YES
43.88
12.40
YES
-0.86
4.78
YES
37.95
12.42
NO
7.89
12.26
NO
7.26
5.21
NO
30.85
9.81
YES
26.76
9.02
YES
32.23
11.45
YES
2.78
8.12
NO
20.69
9.58
YES
12.02
7.31
NO
58.18
14.72
NO
60.33
13.34
NO
35.73
9.68
YES
14.59
7.38
YES
4.83
3.45
NO
15.09
2.89
YES
27.18
11.24
NO
9.12
5.20
NO
8.35
9.04
NO
5.42
4.57
NO
16.33
5.58
YES
28.86
8.20
YES
12.63
7.42
NO
10.04
14.02
NO
19.10
7.53
YES
22.83
7.67
NO
26.78
8.43
NO
25.26
9.44
YES
14.52
8.21
YES
27.54
11.00
YES
36.68
10.12
NO
16.44
6.29
YES
13.80
5.24
YES
26.81
8.32
NO
30.30
13.45
NO
42.73
10.96
YES
2) (3pts, total) Each of the 1499 rows of data (found o
the advertising dollars (in millions) spen
A “highly paid” actor is one who was pai
• Run a regression analysis on sales, u
• For the categorical variable of “High
• When Excel asks the output range (i
• Be sure to include residual plots.
a) (1 pts) Write down the regression eq
let A representing advertising d
b)
(1pt) Suppose the regression mode
and recalling that a highly paid
suggest that using highly paid ac
Yes (using highly paid actor
No (using highly paid actor
c)
(1 pt) Based upon the regression ou
Yes
33.31
19.50
10.31
20.65
-0.92
10.82
33.55
33.94
15.92
7.24
25.27
17.94
23.15
11.19
-0.03
9.67
42.57
19.85
41.09
19.26
22.38
13.35
23.50
23.43
6.61
20.70
21.60
14.13
30.53
25.00
2.70
19.46
19.79
27.52
23.61
12.84
30.36
45.40
13.81
30.49
8.57
19.06
35.25
2.12
17.11
39.05
19.32
11.51
8.80
4.05
8.71
9.57
4.59
9.08
12.57
9.80
7.02
9.17
8.67
12.37
7.52
-0.01
3.43
10.74
8.81
12.94
5.57
8.87
6.39
11.77
9.35
7.96
8.30
8.08
11.75
13.44
7.56
6.13
6.46
6.44
15.58
7.87
8.31
9.89
14.39
11.01
8.95
8.31
9.14
12.17
4.43
7.78
11.47
7.72
YES
NO
NO
YES
NO
NO
YES
YES
YES
NO
YES
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
YES
NO
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
YES
NO
YES
NO
NO
NO
YES
NO
NO
NO
YES
1.05
12.44
9.67
36.80
19.24
47.54
32.94
19.43
19.99
6.88
22.66
15.52
33.37
14.09
14.53
17.81
14.66
18.28
13.85
23.77
12.78
55.98
15.92
20.55
41.74
17.03
43.03
26.53
14.25
15.15
36.44
15.74
24.04
0.84
19.82
42.91
31.03
36.18
39.75
6.07
15.74
17.20
5.91
15.10
14.74
32.55
27.88
11.02
9.88
8.25
10.13
6.27
11.71
9.25
8.52
11.19
3.99
8.97
16.61
7.74
8.10
3.59
10.32
11.30
11.54
12.88
14.16
7.87
16.74
8.17
6.17
12.57
9.77
12.08
7.94
10.22
8.91
9.90
6.07
10.59
10.16
7.35
12.02
7.09
8.10
5.85
8.50
8.89
8.24
10.76
6.87
5.94
7.80
14.27
YES
NO
YES
YES
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
YES
YES
YES
NO
NO
NO
NO
YES
NO
YES
YES
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
YES
YES
YES
YES
NO
NO
YES
YES
YES
YES
YES
23.10
22.64
12.88
22.32
29.30
10.91
5.89
16.49
19.76
25.80
21.28
12.17
20.45
30.86
13.15
16.16
27.87
27.45
28.60
40.76
7.56
16.30
18.83
36.96
16.08
18.92
43.02
5.62
11.55
6.74
15.06
22.23
27.01
33.08
18.09
9.66
35.18
14.51
14.84
16.64
8.18
15.60
22.95
35.33
13.54
31.65
14.44
8.33
9.54
5.34
6.47
11.72
11.16
6.06
8.67
8.18
8.56
10.43
5.60
10.90
10.91
4.30
9.14
11.44
10.84
11.88
18.01
5.47
10.61
8.14
12.38
12.76
4.95
12.54
5.51
6.49
12.49
6.84
10.15
10.79
14.16
8.05
9.84
11.55
15.99
6.31
10.75
6.03
6.32
8.44
8.52
12.09
12.53
4.63
YES
NO
YES
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
NO
NO
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
YES
NO
YES
NO
YES
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
NO
NO
NO
YES
24.94
15.93
23.04
12.21
25.90
19.59
13.13
28.78
-2.11
50.30
35.27
21.72
11.15
29.33
-0.88
55.39
19.29
34.44
29.72
20.42
23.15
13.02
15.13
7.93
11.44
10.00
18.61
27.71
31.78
25.44
8.84
35.77
26.33
17.81
39.58
26.78
24.32
25.05
29.78
15.96
-18.13
37.33
10.83
5.79
21.08
8.91
16.49
8.59
10.51
6.64
10.64
8.35
12.52
6.02
14.12
3.90
14.42
12.54
11.10
7.92
9.35
7.19
12.09
6.38
12.72
7.07
11.57
10.75
5.43
5.12
9.60
4.63
9.02
10.56
10.47
16.61
8.63
6.61
10.48
8.47
5.71
9.57
12.65
6.30
8.44
13.08
12.34
12.60
12.95
7.34
12.90
6.75
9.88
7.42
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
YES
NO
NO
YES
NO
YES
YES
YES
YES
NO
YES
YES
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
YES
NO
NO
YES
NO
YES
7.36
10.70
74.85
23.89
29.13
18.85
24.02
21.36
9.95
24.08
62.33
28.31
23.18
22.35
26.64
-0.69
17.49
22.18
26.51
-4.32
12.45
31.74
19.90
10.73
0.86
33.43
4.12
20.43
34.31
19.19
-1.17
24.33
42.30
9.67
33.15
23.76
26.73
54.14
14.11
17.37
15.42
40.23
35.98
15.54
8.52
27.51
20.73
8.53
4.39
14.34
7.60
11.58
7.47
8.48
11.81
8.96
7.48
15.45
7.86
9.54
7.47
7.38
10.32
6.39
8.10
8.32
6.56
4.95
10.20
13.12
9.71
6.23
11.84
6.00
6.61
10.99
9.81
10.63
9.94
10.01
1.88
12.38
10.76
8.40
13.63
8.44
11.68
8.17
14.35
10.48
5.59
1.22
13.92
8.75
NO
YES
YES
NO
YES
YES
NO
NO
NO
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
YES
YES
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
YES
YES
YES
YES
NO
YES
YES
YES
NO
YES
YES
YES
YES
YES
NO
19.18
46.13
24.69
23.28
20.04
28.79
11.99
8.30
18.58
29.72
36.97
22.75
33.17
29.04
26.62
24.75
55.11
15.90
22.75
10.14
22.65
23.85
21.06
36.77
21.81
23.52
-0.93
16.15
14.18
12.69
-1.49
16.00
7.18
39.79
24.02
22.97
17.31
9.22
21.01
26.21
1.82
38.66
11.24
30.31
35.38
24.79
10.36
5.22
11.30
6.98
5.49
13.43
13.99
7.61
6.72
12.62
10.55
11.77
5.97
10.02
11.04
10.57
9.74
11.55
6.88
5.71
13.10
10.10
7.57
10.42
8.96
11.41
9.11
10.01
11.13
6.79
6.29
10.51
8.70
10.94
12.33
8.73
11.64
8.95
6.72
10.12
11.32
0.76
11.82
8.73
14.01
14.46
12.07
3.48
YES
YES
YES
NO
YES
YES
NO
NO
NO
YES
NO
YES
YES
YES
NO
NO
NO
NO
YES
NO
NO
NO
YES
YES
YES
YES
YES
YES
NO
NO
NO
NO
YES
YES
NO
NO
NO
NO
YES
NO
NO
YES
NO
NO
YES
YES
YES
21.99
18.56
35.21
16.57
17.77
8.97
38.84
26.75
30.21
5.61
23.72
27.61
-0.87
57.07
31.84
22.93
37.23
31.28
40.81
25.39
7.08
16.49
8.54
22.24
18.37
34.33
6.69
0.26
36.29
16.75
34.54
11.94
18.54
40.26
28.26
8.39
4.75
6.98
22.11
3.01
24.99
18.11
16.00
18.74
7.64
14.90
33.59
8.06
8.42
10.97
5.98
8.93
7.98
17.05
9.69
11.64
7.86
6.98
8.91
7.09
16.23
10.54
9.29
12.36
11.07
10.63
9.69
9.51
5.34
6.12
15.21
5.31
7.36
14.09
8.90
12.20
6.00
12.28
6.58
7.78
10.24
11.41
5.98
2.88
13.52
10.96
10.63
5.53
6.34
3.83
6.97
6.67
7.07
14.90
YES
NO
YES
YES
NO
NO
NO
NO
YES
NO
YES
YES
NO
YES
NO
YES
YES
NO
YES
NO
YES
YES
NO
YES
NO
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
YES
YES
NO
YES
NO
1.93
26.53
9.05
21.49
13.18
5.84
2.35
7.06
33.81
31.80
12.55
44.45
54.13
23.37
51.60
9.55
8.45
22.82
16.56
4.25
1.41
7.64
23.45
24.09
14.58
11.10
19.11
30.47
11.00
15.16
19.49
3.10
17.70
10.31
19.71
-2.65
12.95
1.87
57.47
13.84
8.61
38.73
24.91
34.25
42.52
51.52
19.75
9.54
8.18
10.29
10.99
5.87
6.66
1.17
5.59
13.65
10.50
8.05
13.60
13.12
10.46
10.50
3.94
11.37
9.57
6.10
8.78
11.85
4.84
12.56
8.63
9.01
5.86
10.20
9.63
8.93
5.52
7.27
1.90
5.20
7.20
10.50
12.95
7.47
8.19
13.52
6.30
14.22
11.67
8.85
10.67
10.12
11.81
6.88
NO
YES
NO
NO
YES
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
YES
NO
NO
NO
YES
YES
YES
YES
NO
YES
NO
NO
NO
YES
NO
YES
NO
NO
YES
YES
NO
NO
NO
NO
YES
YES
YES
NO
YES
NO
25.69
15.65
12.47
30.23
33.04
26.16
12.16
28.52
8.03
5.04
26.45
10.20
30.61
19.04
20.97
72.05
27.80
11.41
14.49
7.60
39.62
24.13
0.24
16.66
4.81
19.66
43.57
13.59
23.51
21.69
24.07
7.02
54.50
30.11
18.42
17.18
21.01
23.99
51.36
20.80
32.30
20.73
10.82
26.58
4.87
21.05
13.76
8.80
6.05
2.56
10.08
11.04
11.60
9.18
9.96
2.37
6.08
6.36
6.72
7.54
6.36
12.66
13.48
12.94
5.87
4.51
7.49
11.50
13.55
13.62
10.70
4.86
8.28
11.19
10.44
11.86
7.53
11.62
3.63
13.90
7.63
7.52
4.90
8.96
9.54
12.28
7.15
10.60
4.55
9.34
10.88
8.01
10.08
9.13
YES
YES
YES
YES
YES
YES
NO
NO
NO
NO
YES
NO
YES
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
NO
NO
29.79
40.63
19.13
30.43
31.41
9.94
4.50
18.94
40.95
25.59
10.36
11.97
38.87
48.36
21.62
27.92
40.13
3.23
47.17
13.35
18.08
12.78
11.44
11.17
14.16
10.17
20.08
29.87
20.84
14.29
18.28
19.39
16.72
25.38
17.52
24.45
18.59
31.22
9.96
33.05
11.04
19.71
14.76
20.59
19.83
11.53
23.33
11.33
16.03
8.18
9.72
14.68
7.65
5.22
7.55
12.09
11.21
5.71
5.04
11.95
15.54
10.75
7.58
9.87
0.46
12.62
9.75
10.42
8.26
7.02
9.09
5.76
13.50
9.59
10.97
6.55
6.50
9.28
5.31
10.69
12.28
4.80
12.46
14.47
12.70
10.71
11.30
6.35
7.07
5.36
7.48
8.49
7.97
11.85
NO
YES
NO
YES
YES
NO
NO
YES
YES
NO
NO
NO
YES
NO
NO
YES
YES
YES
YES
NO
NO
YES
NO
YES
NO
YES
YES
YES
YES
NO
YES
YES
YES
YES
YES
NO
NO
YES
NO
YES
NO
YES
NO
YES
YES
YES
NO
20.24
21.23
16.01
17.19
27.98
14.82
21.36
28.82
18.62
22.87
24.02
32.05
32.68
12.71
27.79
50.85
13.46
10.54
16.89
9.52
38.65
19.50
17.98
16.73
17.06
9.59
7.79
55.92
6.98
35.79
24.27
24.74
26.70
22.68
20.76
10.28
14.07
13.53
38.35
9.32
1.97
11.90
12.93
17.97
24.51
35.08
34.28
10.80
7.78
15.05
6.62
8.78
5.09
8.98
17.37
8.31
8.50
12.87
11.40
8.63
7.95
8.00
12.30
7.33
6.50
11.37
5.17
13.48
6.50
7.16
7.89
10.69
4.68
4.82
14.78
5.65
10.40
9.42
11.47
10.46
9.26
6.47
4.67
12.35
8.11
10.67
7.90
6.81
4.54
5.80
10.05
9.23
15.54
11.55
NO
YES
NO
NO
NO
YES
YES
YES
YES
YES
NO
NO
NO
YES
YES
YES
NO
NO
YES
NO
NO
YES
NO
YES
NO
NO
YES
YES
NO
NO
NO
NO
YES
YES
YES
NO
NO
YES
YES
NO
NO
NO
NO
YES
YES
YES
NO
12.24
11.48
13.91
26.57
24.52
22.01
35.72
8.61
12.48
14.28
-6.62
19.46
-1.38
28.12
-0.37
9.63
10.58
20.87
8.70
40.98
6.85
11.18
13.33
20.83
14.32
22.68
31.98
18.70
20.16
19.00
18.67
49.46
8.70
28.24
18.58
21.91
17.20
18.81
28.00
47.60
8.49
18.55
43.67
15.66
16.19
24.48
29.67
7.42
11.00
11.42
9.85
10.83
10.21
9.61
6.82
6.00
6.46
13.43
7.72
5.44
5.42
11.48
5.41
5.67
8.70
10.94
10.01
3.69
5.03
8.31
9.73
4.18
11.40
9.33
8.73
8.20
5.47
7.70
11.82
9.25
10.35
9.86
8.38
10.97
9.90
9.55
13.31
6.13
7.70
10.41
6.75
10.31
10.86
9.48
NO
YES
NO
NO
YES
NO
YES
YES
NO
YES
NO
YES
NO
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
YES
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
YES
NO
YES
YES
NO
NO
NO
NO
YES
YES
NO
8.46
19.91
37.63
36.14
17.00
13.41
27.86
23.79
20.03
13.09
12.83
20.06
16.36
7.53
-11.47
6.32
-0.63
5.64
9.50
39.42
14.83
19.61
32.41
12.72
7.88
20.55
13.94
30.95
15.41
10.82
36.30
24.58
4.26
2.81
28.27
27.11
43.20
9.60
9.61
11.89
21.96
14.73
46.43
20.30
17.62
15.78
9.07
2.70
5.62
10.02
8.50
9.04
5.42
5.57
6.56
7.27
5.28
8.40
8.05
13.81
5.81
10.40
6.04
12.03
8.64
3.38
11.71
13.49
10.97
12.62
9.13
10.41
9.25
7.58
11.95
9.13
6.90
10.43
11.04
9.96
0.63
8.83
10.17
10.06
12.67
8.21
9.50
11.15
8.21
13.34
5.17
8.65
7.90
9.18
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
NO
NO
NO
YES
NO
NO
NO
NO
YES
YES
YES
NO
YES
NO
YES
YES
NO
YES
YES
NO
YES
YES
35.88
6.60
11.27
33.05
7.50
15.09
14.77
20.10
5.39
46.47
22.46
43.28
28.63
21.53
11.57
16.86
15.75
16.65
23.42
12.23
18.11
21.04
20.33
18.85
17.69
29.37
30.11
22.89
24.00
20.18
11.26
18.65
41.15
27.06
34.15
9.60
16.61
14.08
27.67
3.55
12.04
13.00
24.39
19.21
33.41
25.33
18.87
9.59
8.06
6.37
12.69
5.20
10.33
7.78
11.71
4.09
13.20
11.62
12.54
9.77
6.55
10.87
9.77
9.49
8.31
10.93
10.21
7.95
5.99
5.03
7.03
6.64
10.04
7.65
12.50
11.06
10.63
7.56
8.76
14.18
6.97
14.07
7.33
12.81
4.78
10.64
7.17
7.91
6.57
7.88
11.18
8.90
9.77
6.73
YES
NO
NO
NO
NO
YES
YES
NO
YES
YES
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
YES
YES
YES
YES
NO
NO
YES
YES
YES
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
YES
YES
18.39
23.65
30.07
26.78
64.99
17.54
18.37
21.34
31.29
37.26
39.25
7.69
35.44
14.76
6.99
15.37
17.87
19.08
43.52
19.77
5.85
10.95
23.09
14.32
16.18
15.09
34.26
20.50
28.56
25.49
28.63
22.00
54.93
32.47
29.77
23.60
5.82
11.97
53.98
44.21
33.00
22.72
11.43
43.47
8.60
20.03
-0.65
10.08
9.74
8.56
10.89
19.32
4.91
13.86
10.78
10.51
9.44
9.89
2.62
10.11
8.61
6.16
13.50
7.22
7.86
12.80
9.07
4.97
6.87
8.99
7.82
12.94
9.44
12.91
7.98
9.73
12.80
13.04
11.74
16.84
7.88
11.47
8.61
8.44
6.15
15.52
9.19
11.13
10.83
6.81
10.32
2.46
10.40
6.23
YES
NO
NO
YES
NO
YES
NO
YES
YES
YES
YES
YES
YES
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
YES
NO
YES
YES
YES
NO
NO
YES
NO
NO
YES
NO
YES
NO
YES
YES
YES
YES
YES
NO
YES
YES
NO
NO
30.52
13.29
22.58
9.72
16.17
32.53
21.87
17.11
5.28
17.85
33.49
47.23
21.65
11.73
15.59
12.97
12.91
15.17
25.16
10.11
8.74
8.38
33.82
16.34
20.72
27.77
10.84
17.51
46.74
21.44
7.87
24.24
22.33
31.74
15.24
28.35
29.69
15.10
37.20
6.95
18.83
4.20
23.70
40.76
25.49
20.87
18.03
10.90
4.10
7.32
5.84
8.43
9.38
11.87
8.94
6.47
11.34
12.97
13.20
5.67
13.12
8.17
5.24
7.19
8.29
11.27
5.10
9.61
8.45
13.75
9.97
10.38
8.80
9.44
10.01
14.70
8.39
11.78
11.62
9.23
10.51
10.50
11.46
9.71
9.22
9.02
8.01
9.42
9.72
8.04
10.75
12.98
7.44
9.79
NO
YES
YES
YES
NO
YES
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
NO
NO
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
YES
NO
YES
NO
NO
NO
YES
38.70
23.47
25.56
19.03
28.75
5.42
25.80
5.95
26.79
21.34
11.92
14.66
45.83
10.50
22.12
29.14
19.70
26.48
26.72
33.32
24.29
22.66
4.31
6.70
11.38
67.14
9.01
3.46
18.34
19.59
35.90
37.60
25.20
17.86
21.02
11.56
16.03
28.98
7.93
23.52
19.37
3.76
13.28
16.09
41.94
30.76
10.53
10.16
12.52
9.72
9.44
11.27
4.87
9.59
11.80
8.16
6.00
8.08
9.26
10.67
10.77
10.26
10.98
10.54
10.25
11.33
8.88
10.95
8.71
7.17
7.40
10.43
16.00
14.03
12.37
10.84
5.73
11.00
14.64
9.35
7.19
8.65
8.98
5.21
7.57
8.79
8.00
7.49
5.83
5.03
10.08
11.58
8.08
3.09
NO
YES
YES
NO
NO
NO
NO
YES
YES
YES
NO
YES
YES
NO
YES
NO
YES
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
NO
YES
YES
NO
YES
NO
NO
NO
YES
YES
YES
NO
14.85
30.57
22.88
11.41
15.63
21.74
12.77
7.59
10.31
21.63
13.33
26.33
28.15
14.90
22.84
15.41
24.95
17.36
19.37
5.73
18.07
15.69
9.87
26.42
12.18
35.03
6.10
23.50
28.23
37.83
20.77
16.36
13.91
24.44
26.86
22.10
1.28
33.82
21.96
18.00
46.77
17.98
0.06
19.31
54.34
20.92
8.46
6.21
8.59
9.92
5.99
7.03
6.90
11.70
7.21
10.20
10.65
7.61
12.58
10.29
7.30
12.32
7.22
6.81
9.40
2.46
8.52
7.47
8.14
6.31
5.98
6.93
11.69
9.95
9.65
10.55
9.87
8.19
10.84
9.65
9.12
8.68
5.62
4.05
6.40
8.45
8.44
12.73
11.61
8.59
10.57
12.54
7.70
7.36
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
NO
YES
NO
NO
YES
NO
YES
NO
YES
NO
YES
YES
NO
YES
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
YES
YES
YES
YES
NO
NO
YES
NO
NO
YES
NO
YES
YES
9.38
17.12
27.54
26.67
5.82
29.07
41.69
8.36
12.18
23.99
29.55
16.30
16.85
13.76
12.25
24.94
-0.28
29.63
10.73
30.15
18.14
4.32
2.33
19.25
10.13
27.84
12.58
43.20
26.43
27.66
9.11
17.84
40.16
32.61
9.13
3.98
8.66
27.34
12.67
10.78
5.43
12.66
14.66
23.13
5.71
9.92
7.76
7.81
6.07
8.03
8.14
11.06
11.47
13.71
10.73
4.52
7.12
15.55
8.69
8.64
9.66
6.24
10.80
11.46
8.75
8.06
11.83
6.35
2.64
2.52
7.72
9.54
8.66
3.47
11.12
10.72
7.86
9.05
12.74
9.44
13.80
3.82
18.17
12.63
12.63
6.60
5.62
3.05
5.08
8.54
8.71
11.34
3.81
14.18
NO
YES
NO
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
NO
NO
YES
NO
YES
NO
NO
NO
YES
NO
YES
NO
NO
YES
YES
NO
YES
YES
NO
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
YES
NO
NO
YES
NO
19.72
15.64
21.44
11.01
22.01
16.08
13.88
17.23
33.59
10.17
14.87
44.01
21.78
16.66
18.22
23.44
31.57
43.68
33.70
18.96
14.97
2.62
37.45
19.30
15.52
36.65
4.14
20.67
34.19
25.34
25.59
8.24
20.62
9.36
19.21
18.04
15.75
1.28
22.49
9.85
33.09
12.81
28.82
42.43
11.74
13.94
12.65
8.10
5.67
10.78
4.73
7.24
3.42
7.41
7.64
10.56
5.03
5.90
11.92
10.18
11.31
7.22
5.73
14.46
12.25
14.00
8.77
7.58
3.88
8.01
9.43
7.80
10.33
3.01
10.24
11.02
10.69
6.34
7.70
6.78
6.88
8.98
9.15
6.21
0.76
7.15
7.07
7.96
5.60
7.11
12.45
8.07
7.19
6.40
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
YES
YES
YES
NO
YES
YES
NO
YES
NO
YES
NO
NO
YES
NO
YES
YES
NO
YES
YES
YES
NO
NO
YES
NO
NO
YES
YES
NO
NO
NO
NO
YES
NO
NO
NO
YES
NO
19.28
32.04
18.98
17.25
23.55
12.18
11.07
26.30
5.97
22.66
12.94
16.19
29.73
24.19
12.55
35.15
22.12
26.87
17.75
17.28
12.58
6.56
9.56
24.63
14.67
30.34
33.42
35.38
10.01
20.18
15.96
23.84
29.19
34.33
9.02
6.68
8.36
5.67
35.01
27.65
22.03
34.18
22.05
0.33
3.23
8.01
19.04
9.73
12.02
10.18
9.95
7.78
5.69
8.10
11.73
11.29
9.74
8.95
9.16
11.22
9.65
2.80
16.58
7.59
8.44
5.43
14.05
7.70
6.89
4.42
9.26
12.25
8.92
10.19
11.77
9.57
10.91
5.99
4.95
10.06
8.50
5.71
4.37
6.64
8.02
8.98
10.05
9.79
12.23
10.93
0.08
7.47
3.17
11.74
YES
YES
NO
YES
NO
NO
NO
YES
NO
YES
YES
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
NO
NO
YES
YES
YES
YES
NO
YES
NO
NO
YES
YES
YES
NO
YES
YES
NO
YES
NO
YES
YES
NO
NO
YES
YES
YES
19.15
8.98
6.90
20.10
11.83
14.78
27.74
23.19
9.00
12.42
12.48
20.26
27.85
16.63
17.71
7.35
19.11
25.99
5.64
21.68
12.90
14.37
20.11
6.20
23.13
3.82
9.07
17.59
19.85
16.24
14.29
7.37
24.44
13.44
16.00
31.09
30.47
31.71
12.30
25.44
18.12
43.93
24.43
10.82
30.69
3.33
3.09
8.35
8.06
6.81
10.27
9.07
13.22
9.42
9.91
5.36
1.76
7.76
6.28
13.58
6.43
13.46
9.89
9.13
14.17
3.23
9.17
8.77
4.94
8.16
9.22
11.27
9.68
7.26
11.59
11.30
7.11
10.98
1.97
8.62
6.34
10.32
8.62
10.02
9.64
7.51
8.91
3.91
8.38
7.21
8.39
10.61
10.07
6.66
NO
NO
YES
NO
NO
NO
YES
NO
NO
YES
YES
YES
YES
NO
NO
YES
NO
YES
NO
NO
NO
YES
YES
YES
NO
YES
NO
NO
YES
YES
NO
YES
YES
YES
YES
YES
YES
NO
NO
YES
YES
YES
NO
NO
NO
NO
NO
24.18
37.19
49.12
27.01
30.38
0.89
21.63
29.30
7.57
23.06
37.76
2.63
22.14
31.94
12.92
21.20
16.36
37.23
10.55
25.77
13.92
12.13
18.66
23.48
19.58
17.61
6.71
13.56
41.47
29.55
12.40
9.14
34.46
17.45
10.76
13.75
1.60
17.99
26.13
25.99
37.69
27.54
9.82
27.73
9.51
20.30
49.72
10.87
8.67
14.97
8.66
12.18
0.90
12.34
9.60
6.17
7.67
13.57
6.37
11.88
8.75
5.58
7.22
8.96
12.02
9.88
8.14
7.86
4.40
7.31
9.10
10.02
11.45
3.07
5.68
12.01
8.37
6.18
10.97
9.58
7.20
9.99
10.64
7.95
5.99
9.96
10.37
11.51
7.06
4.21
15.92
5.72
11.21
16.33
YES
NO
YES
NO
NO
NO
NO
YES
NO
YES
NO
NO
NO
YES
NO
NO
NO
YES
YES
NO
NO
NO
YES
YES
NO
NO
YES
YES
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
YES
YES
YES
YES
NO
NO
YES
9.87
20.35
6.46
37.58
30.18
24.07
37.40
15.81
48.68
29.35
41.70
17.11
18.46
41.38
1.62
26.99
19.96
16.07
32.80
10.35
18.23
17.61
18.85
22.29
17.32
18.77
32.16
43.07
5.31
0.90
16.68
-6.95
15.32
10.54
7.68
27.20
21.19
21.42
37.99
27.52
9.99
32.23
21.77
22.35
11.61
45.47
9.67
13.80
8.33
13.27
12.66
10.12
9.06
9.34
4.72
13.42
11.55
11.02
9.30
9.70
13.79
9.34
7.20
10.70
8.35
15.77
6.83
8.44
10.14
6.97
8.92
7.71
11.79
10.70
10.55
7.48
2.50
4.55
6.72
6.99
6.67
8.44
7.36
8.31
7.36
11.32
10.82
7.60
6.64
8.07
5.87
8.23
10.08
8.02
YES
NO
NO
YES
YES
YES
YES
NO
YES
NO
YES
NO
YES
NO
YES
NO
YES
NO
NO
YES
YES
NO
YES
YES
NO
NO
YES
YES
NO
NO
NO
NO
NO
YES
YES
YES
NO
NO
YES
NO
YES
YES
NO
YES
NO
YES
YES
21.63
26.08
10.48
16.54
17.13
21.28
30.21
23.57
16.08
15.02
20.19
17.13
39.95
25.02
36.30
22.17
17.03
8.12
16.94
17.81
22.60
30.41
38.97
13.24
23.65
37.43
25.87
24.88
14.94
12.13
-3.06
12.51
15.37
5.47
10.17
33.02
11.42
31.95
33.29
23.97
24.22
15.86
7.45
3.10
26.96
23.49
26.66
7.13
10.98
6.93
5.10
8.59
6.29
11.61
8.85
7.33
6.27
5.22
3.25
9.84
8.93
9.11
9.16
13.12
5.68
8.82
10.25
13.96
11.28
11.33
13.04
9.03
11.26
6.48
7.93
9.12
11.69
4.93
6.73
12.97
2.32
4.70
6.75
9.27
12.68
11.73
6.77
9.19
3.58
7.97
5.85
10.96
8.49
9.99
NO
NO
YES
YES
NO
NO
YES
NO
YES
YES
YES
YES
NO
NO
NO
NO
NO
NO
YES
YES
YES
NO
YES
NO
NO
YES
YES
YES
YES
YES
NO
NO
YES
NO
NO
YES
NO
NO
NO
YES
YES
YES
YES
NO
YES
YES
YES
28.64
12.15
11.71
16.72
-0.62
45.03
7.70
23.56
33.47
33.93
16.44
29.95
18.99
21.90
11.90
45.47
4.51
47.88
58.95
21.65
9.40
19.41
12.94
10.75
28.55
3.79
14.97
32.33
17.78
40.77
16.83
44.90
6.90
21.47
10.63
13.49
27.28
11.86
34.15
10.58
6.20
40.47
17.26
18.14
20.11
13.37
4.31
7.76
8.41
6.15
11.48
9.79
11.98
14.10
13.76
11.27
16.25
8.52
10.20
9.65
6.73
7.37
12.17
6.64
12.22
15.92
8.70
3.31
9.59
6.65
4.62
7.80
9.72
14.15
9.73
7.74
10.14
8.60
10.67
2.97
10.23
4.87
10.55
10.35
13.41
10.65
7.59
8.45
12.50
6.48
8.02
7.80
6.88
6.45
YES
YES
NO
YES
NO
YES
NO
NO
NO
NO
NO
YES
YES
YES
YES
YES
NO
YES
NO
NO
YES
NO
NO
YES
YES
NO
NO
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
YES
NO
YES
YES
NO
NO
YES
NO
NO
1.35
10.43
10.70
29.33
20.43
20.86
7.38
22.91
6.60
15.12
28.08
15.11
7.60
41.88
-1.56
10.16
24.78
14.26
53.94
30.27
24.16
16.98
14.61
34.22
14.19
20.55
12.83
36.82
18.50
20.16
34.30
28.32
10.92
16.85
10.95
9.64
21.08
11.87
8.79
10.30
23.15
49.30
39.39
5.84
13.25
23.15
12.46
0.71
7.10
5.51
12.53
11.39
9.00
8.26
6.86
2.67
5.60
14.08
8.69
5.43
7.78
13.71
6.58
13.78
8.87
11.37
13.99
11.36
7.72
4.66
11.75
8.24
5.82
5.36
9.29
7.74
7.20
16.00
11.02
8.45
6.01
1.74
8.03
8.11
6.56
4.52
10.67
10.97
11.57
9.93
8.71
11.59
8.72
5.18
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
NO
YES
NO
YES
NO
YES
NO
YES
NO
YES
YES
YES
NO
NO
YES
NO
YES
NO
YES
YES
NO
NO
YES
NO
NO
YES
NO
NO
YES
19.38
11.04
11.01
17.77
25.96
13.81
19.74
17.90
10.05
13.40
26.32
35.51
22.54
13.52
20.13
21.54
25.66
13.22
13.08
20.56
46.25
46.79
5.90
7.82
18.90
20.13
24.07
26.92
28.76
6.67
13.42
19.00
21.91
11.30
11.70
10.85
12.15
15.21
25.61
22.98
40.40
-19.74
21.76
14.41
20.81
21.34
16.81
14.35
7.14
3.41
6.63
7.52
9.76
6.53
9.86
9.78
5.76
10.82
14.01
7.56
8.90
9.83
9.76
5.86
5.68
11.27
6.20
9.73
13.07
14.64
10.68
8.36
11.42
9.37
12.16
9.30
15.75
8.73
7.62
8.29
7.30
4.15
11.11
5.97
6.59
8.94
9.03
12.37
16.28
7.88
9.12
8.19
8.16
11.39
YES
NO
NO
NO
YES
YES
NO
YES
NO
NO
NO
YES
YES
NO
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
NO
YES
NO
YES
YES
NO
YES
YES
NO
NO
YES
NO
YES
YES
NO
YES
YES
YES
YES
YES
13.42
18.04
19.63
1.21
35.62
16.40
29.30
10.84
11.34
34.05
16.95
24.82
15.32
11.31
20.43
13.37
34.35
38.75
7.08
50.96
17.07
19.19
23.16
29.71
7.10
26.79
24.03
9.49
56.05
40.76
6.09
34.00
9.92
20.32
7.60
9.65
21.21
21.76
14.84
25.67
3.87
31.68
28.15
21.29
32.15
24.85
24.64
5.01
12.95
7.55
8.41
12.02
6.33
6.93
8.97
13.92
11.13
7.95
8.40
10.40
7.89
8.30
5.16
7.82
11.77
4.82
11.63
7.64
7.06
7.21
12.13
10.10
8.53
8.56
3.33
16.91
13.47
3.06
14.75
8.80
8.64
3.38
8.83
6.99
11.92
5.53
9.47
5.29
8.20
9.36
8.23
10.35
9.55
6.21
YES
YES
YES
NO
NO
NO
YES
NO
YES
YES
YES
YES
YES
YES
YES
NO
NO
NO
YES
YES
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
YES
NO
NO
YES
YES
NO
YES
NO
NO
NO
NO
YES
NO
YES
YES
YES
22.71
35.83
13.55
18.81
29.45
1.15
3.59
16.04
-2.58
10.57
19.72
5.92
22.45
5.09
21.90
15.60
23.65
45.30
13.93
24.98
29.75
50.57
14.35
16.22
49.59
18.20
20.93
14.33
32.26
16.35
11.48
26.44
10.65
7.27
11.48
21.82
24.11
13.38
27.42
29.52
20.58
21.32
11.82
13.85
26.51
10.39
21.75
4.84
7.34
10.15
5.31
11.88
2.78
1.38
7.13
13.25
10.39
4.38
7.42
11.61
11.15
7.00
8.33
8.15
12.15
9.16
12.43
9.70
13.38
8.95
9.57
11.96
7.60
6.28
9.04
12.15
7.63
7.03
9.09
6.66
1.39
8.82
9.32
7.63
3.80
9.24
11.88
4.98
13.19
3.74
10.64
8.61
8.53
9.17
YES
YES
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
YES
NO
YES
YES
YES
NO
NO
NO
YES
YES
NO
YES
NO
NO
YES
YES
NO
NO
YES
NO
YES
YES
NO
NO
YES
NO
YES
NO
YES
YES
NO
NO
NO
NO
NO
13.60
7.03
15.10
16.21
11.39
36.04
9.89
10.12
26.81
19.73
7.07
13.16
13.69
26.25
15.58
23.12
30.04
9.20
12.15
3.11
13.21
23.56
27.28
16.01
12.24
20.69
25.82
21.69
3.27
13.42
25.17
20.98
7.05
7.33
5.99
13.37
45.92
21.78
2.60
27.47
28.17
5.94
25.21
17.17
9.86
4.01
8.40
14.54
8.13
9.84
4.87
7.78
9.97
10.68
8.42
12.81
9.67
6.99
7.96
8.03
11.94
6.07
5.18
3.87
2.79
10.09
11.05
7.09
5.04
8.64
9.90
6.51
3.62
5.57
10.68
8.40
4.90
11.59
10.07
7.67
11.71
9.51
7.15
6.08
10.32
12.15
6.42
15.27
NO
YES
NO
NO
NO
YES
YES
YES
NO
NO
NO
NO
NO
NO
NO
YES
YES
NO
NO
NO
YES
NO
YES
YES
NO
NO
NO
NO
NO
NO
YES
NO
NO
YES
NO
YES
YES
NO
YES
NO
YES
YES
YES
YES
1499 rows of data (found on the left, spanning columns A, B and C) depicts the sales of a particular movie (in millions of dollar
ng dollars (in millions) spent on that movie, and whether or not there was a highly paid actor that appeared in the movie.
d” actor is one who was paid more than $5 million.
gression analysis on sales, using the independent variables of “Advertising” and “Highly paid.”
categorical variable of “Highly paid,” treat “NO” as the base case.
xcel asks the output range (i.e. where you want to output the regression analysis), choose cell G30.
to include residual plots.
rite down the regression equation that results from running Excel’s regression analysis. Let S represent sales,
A representing advertising dollars, and let H represent the variable corresponding to a highly paid actor, with base case of “NO
ppose the regression model accurately predicts a movie’s revenue. Recalling that profit equals revenue minus cost,
recalling that a highly paid actor is one who by definition costs more than $5 million to obtain, does the regression analysis
gest that using highly paid actors adds to the movie’s bottom line profit total? Highlight your answer.
Yes (using highly paid actors increases movie’s profit)
No (using highly paid actors does NOT increase movie’s profit)
ased upon the regression output, do the residuals appear to be independent of the “Advertising” variable? Highlight your ans
No
ular movie (in millions of dollars),
id actor, with base case of “NO.”
g” variable? Highlight your answer
3) (2 points) Suppose that you run a regression analysis of summer temperatures in Iowa, based on the variab
(measured in the number of hours away from noon, so 10AM and 2PM would both be recorded as
regression equation that results from this is as follows:
What would be the fitted regression equation if you had instead used North as the base case for th
(Your answer should include some amount of work shown. The answer will be a single equation, bu
es in Iowa, based on the variables of Region (either North, South, East, West) and Time of day the temperature was recorded
PM would both be recorded as 2). Suppose you let West be the base case for the variable, Region, and suppose the fitted
Temperature = 80 + 2*South – 4*North + 1*East – 3*Time.
d North as the base case for the variable, Region?
wer will be a single equation, but you need to include enough work/explanations to indicate how you arrived at that answer.)
the temperature was recorded
on, and suppose the fitted
w you arrived at that answer.)
4) (2 points, total) Suppose you wish to maximize the value of 2y+8x, subject to the following constraints:
y≤4
y ≥ x+1
x+y ≤ 6
Also assume non-negativity
Set up and solve this linear program using Excel’s solver so that you maximize the value of 2y+
Place your answer of this maximum value in the highlighted green cell, below.
t you maximize the value of 2y+8x subject to the above constraints.
5) (4 points in total, parts a through c, scroll down to see all parts)
Suppose that you own a pizza shop and make 3 different types of pizzas, using 4 varieties of
Also, each pizza requires certain amounts of the various cheeses but you only have a certain
All this information appears in the table, below. (The 16 numbers in cells B9:E12 represent o
Lastly, you are under contract with the company that provides your gorgonzola cheese, and t
across all made pizzas must be at least as much as the sum total of ounces of all other (non-g
Cheddar
Amazing Saucer
Queso-rific
Cheddar Time
Mozzarella Gorgonzola
Swiss
1
2
13
0
13
0
13
5
12
500 avail. 300 avail. 800 available 200 avail.
3 $10 revenue
5 $8 revenue
1 $14 revenue
In what follows, you’ll be setting up and solving a linear program (LP) which reflects the abov
in order to maximize your revenue. Assume that any unused cheese is wasted, and assume t
make fractions of pizzas, i.e. it’s fine if the solution shows making 3.437 pizzas (for example)
• Let the variable A represent the number of Amazing Sauacer pizzas that you make
• Let the variable Q represent the number of Queso-rific pizzas that you make
• Let the variable C represent the number of Cheddar Time pizzas that you make
a) (1pt) Write down the objective function, as a mathematical expression in term of the va
Here you are not coding the Excel cells, but instead writing a mathematical expression, i.e
b) (1 pt) Write down all applicable constraints for this problem as mathematical expressio
Here you can use = for “greater than or equal.” Your answ
but is instead a list of mathematical expressions, i.e. it’s what you’d write on paper if you w
c) (2 pts) What is the maximum revenue that is achievable while still satisfying all of the pr
(To receive full credit, you must properly code your workbook and solve this with Excel’s So
hich reflects the above scenario and your attempt to bake the appropriate quantities of each pizza
wasted, and assume that all baked pizzas will end up being purchased. Also, assume that you can
matical expression, i.e. it’s what you’d write on paper if you were writing the objective function.
6) (6 points, total) A company will need to produce P units of a product next quarter, where P is uncertain bu
Note that since P is continuous, we are allowing for fractions/decimals of product to be prod
•
Option 1: Its first option is to produce the units themselves for a per-unit cost of $125 and a fixe
• Option 2: Its second option is that it can outsource the production to another company for a fix
chance that F will be $70,000 and a 90% chance that F will be $35,000), as well as a per-unit cost, C
a) (2 pts) Let X represent the cost incurred by the company if it takes Option 1 and Let Y represent the cos
Note that there should be no Excel formula’s here, just write down what X and Y equal in terms of
X=
Y=
b) (3 pts) Run a Monte Carlo Simulation with 1000 trials simulating the values of X and Y.
Place your MCS on this same sheet, below line 25
c) (1 pts) Based upon the results of your simulation in (b), what percentage of the time does your simulat
RUN YOUR MCS HERE
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uarter, where P is uncertain but follows a (continuous) uniform distribution with minimum value 800 and maximum value 170
decimals of product to be produced. The company has two options for how it can produce these P units:
on to another company for a fixed cost of F (which is an international surcharge that varies from time to time, and there is a 1
00), as well as a per-unit cost, C, which is uncertain but normally distributed with mean $175 and standard deviation $12.
e of the time does your simulation tell you that it is cheaper for the company if they produce the product themselves?
ue 800 and maximum value 1700.
m time to time, and there is a 10%
7) (1 pt) Consider the following situation: You run a catering business and every Wednesday evening you deli
You’ve noticed that you frequently have leftovers, and one of your employees who delivers the leftove
You, however, have been recording the quantity of leftovers (measured in pounds) that exist after eac
that you’ve recorded lead you believe that your employee is incorrect. Since the quantity of leftovers
your employee is incorrect. To do this, you recall the techniques learned from your fondly remembere
Suppose you wish to test your hypothesis using your sample data from these 36 most recent Wednesd
You want to test the hypothesis with an alpha of .05, and you discover that the test statistic is positive
What was the sample average from your data? (Must show work/properly coded Excel cell/etc.)
Hint: Based on the information in the problem, what is the test statistic? Now look at the equation for
y Wednesday evening you deliver the same dinner (identical food and quantity) to the same executives at a particular compan
loyees who delivers the leftovers to a local shelter told you she thought there were about 10 pounds of leftovers per dinner, o
in pounds) that exist after each of these Wednesday night dinners. You’ve been doing this now for 36 weeks and the sample
Since the quantity of leftovers exhibits some amount of randomness, you decide to test your hypothesis with the goal of prov
these 36 most recent Wednesday night dinners, and suppose you find that the sample standard deviation of this data is 3 pou
ounds of leftovers per dinner, on average.