Assignment:
Q1: Solar Energy in Different Weather: A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table. Use a).05 significance level to test the claim that the mean voltage reading is the same for the three different types of day. Is there sufficient evidence to support a claim of different population means? We might expect that a solar system would provide more electrical energy on sunny days than on cloudy or rainy days. Can we conclude that sunny days
Result in greater amount of electrical energy?
|
Sunny Days
|
Cloudy Days
|
Rainy Days
|
|
|
13.5
13.0
13.2
13.9
13.8
14.0
|
12.7
12.5
12.6
12.7
13.0
13.0
|
12.1
12.2
12.3
11.9
11.6
12.2
|
Interpreting a Computer Display. In exercise 8 use the Excel display, which results from the scores listed in the accompanying table. The sample data are SAT scores on the verbal and math portions of SAT-I and are based on reported statistics from the College Board. The "Columns" variable is SAT (verbal/math) and the "Sample" variable is gender.
Q2: Interaction Effect: Test the null hypothesis that SAT scores are not affected by an interaction between gender and test verbal/math) what do you conclude?
Verbal
|
Female 646 539 348 623 478 429 298 782 626 533
|
|
Male 562 525 512 576 570 480 571 555 519 596
|
|
|
|
|
|
Math
|
Female 484 489 436 396 545 504 574 352 365 350
Male 547 678 464 651 645 673 624 624 328 548
|
Anova
|
|
|
|
|
|
|
|
Source of Variation
|
SS
|
df
|
MS
|
F
|
P-value
|
F crit
|
|
Sample
|
52635.03
|
1
|
52635.03
|
5.029517
|
0.031169
|
4.113161
|
|
Columns
|
6027.025
|
1
|
6027.025
|
0.57591
|
0.45286
|
4.113161
|
|
Interaction
|
31528.22
|
1
|
31528.22
|
3.012666
|
0.09117
|
4.113161
|
|
Within
|
376748.1
|
36
|
10465.23
|
|
|
|
|
|
|
|
|
|
|
|
|
Total
|
466938.4
|
39
|
|
|
|
|
Q3: For U.S. presidents and the popes and British monarchs since 1690, the accompanying table lists the numbers of years that they lived after their inauguration, election, or coronation. Use boxplots and analysis of variance to determine whether the survival times for the different groups differ. Conduct the analysis of variance by using Excel. Obtain printed copies of the computer displays and write your observation and conclusions.
| Presidents |
|
Popes |
|
Kings and Queens |
| Washington |
10 |
A.lex VIII |
2 |
James II |
17 |
| J. Adams |
29 |
Innoc XII |
9 |
Mary II |
6 |
| Jefferson |
26 |
Clem XI |
21 |
William III |
13 |
| Madison |
28 |
Innoc XIII |
3 |
Anne |
12 |
| Monroe |
15 |
Ben XIV |
6 |
George I |
13 |
| J.Q. Adams |
23 |
Clem XII |
10 |
GerogeII |
33 |
| Jackson |
17 |
Ben XIV |
18 |
George III |
59 |
| Van Buren |
25 |
Clem XIII |
11 |
Geroge IV |
10 |
| Harrison |
0 |
Clem XIV |
6 |
William IV |
7 |
| Tyler |
20 |
Pius VI |
25 |
Victoria |
63 |
| Polk |
4 |
Pius VIII |
23 |
Edward VIII |
9 |
| Taylor |
1 |
Leo VII |
6 |
George VI |
25 |
| Filmore |
24 |
Pius VIII |
2 |
|
36 |
| Pierce |
16 |
Greg XVI |
15 |
|
15 |
| Buchanan |
12 |
Pius IX |
32 |
|
|
| Lincoln |
4 |
Leo XIII |
25 |
|
|
| A. Johnson |
10 |
Pius X |
11 |
|
|
| Grant |
17 |
Ben XV |
8 |
|
|
| Hayes |
16 |
Pius XI |
17 |
|
|
| Garfield |
0 |
Pius XII |
19 |
|
|
| Arthur |
7 |
John XXIII |
5 |
|
|
| Cleveland |
24 |
Paul VI |
15 |
|
|
| Harrison |
12 |
John Paul I |
0 |
|
|
| Mckinley |
4 |
|
|
|
|
| T. Roosevelt |
18 |
|
|
|
|
| Taft |
21 |
|
|
|
|
| Wilson |
11 |
|
|
|
|
| Harding |
2 |
|
|
|
|
| Coolidge |
9 |
|
|
|
|
| Hoover |
36 |
|
|
|
|
| F.Roosevelt |
12 |
|
|
|
|
| Truman |
28 |
|
|
|
|
| Kennedy |
3 |
|
|
|
|
| Eisenhower |
16 |
|
|
|
|
| L.Johnson |
9 |
|
|
|
|
| Nixon |
25 |
|
|
|
|
| 478 |
429 |
298 |
782 |
626 |
533 |
| 570 |
480 |
571 |
555 |
519 |
596 |
|
|
|
|
|
|
|
|
|
|
|
|
| 545 |
504 |
574 |
352 |
365 |
350 |
| 645 |
673 |
624 |
624 |
328 |
548 |
| Placebo Group |
10-mg Treatment Group |
20-mg Treatment Group |
| 77 |
67 |
72 |
| 61 |
48 |
94 |
| 66 |
79 |
57 |
| 63 |
67 |
63 |
| 81 |
57 |
69 |
| 75 |
71 |
59 |
| 66 |
66 |
64 |
| 79 |
85 |
82 |
| 66 |
75 |
34 |
| 75 |
77 |
76 |
| 48 |
57 |
59 |
| 70 |
45 |
53 |
| $1,927.48 |
$27,902.31 |
86,241.90 |
72,117.46 |
81,321.75 |
97,473.96 |
| $93,249.11 |
89,658.16 |
87,776.89 |
$92,105.83 |
79,949.16 |
87,602.93 |
| 96,879.27 |
91,806.47 |
84,991.67 |
$90,831.83 |
93,766.67 |
88,336.72 |
| $94,639.49 |
83,709.26 |
96,412.21 |
$88,432.86 |
71,552.16 |
|
The above table are used to answer the below questions:
Q4: In the trail of State of Arizona vs. Wayne James Nelson, the defendant was accused of issuing checks to a vendor that did not really exist. The amounts of the checks are listed below in order by row.
Analyzing the Results Do the leading digits conform to Benford's law described in the Problem?
When testing for goodness of fit with the proportions expected with Benford's law, it is necessary to combine categories because not all expected values are at least 5. Use one category with leading digits of 1, a second category with leading digits of 2, 3, 4, 5, and the third category with leading category with leading digits of 6, 7, 8, and 9. Are the expected values for these three categories all at least 5? Is there sufficient evidence to conclude that the leading digits on the checks do not conform to Benford's Law? Apart from the leading digits, are there any other patterns suggesting that the check amounts were created by the defendant instead of being the result of typical and real transactions? Based on the evidence if you were a juror, would you conclude that the check amounts are the result of fraud? What would be one argument that you might present if you were the attorney for the defendant?