Statistics assignment 6

STAT 212 – Assignment 6

Data Description and Background

In this assignment we will continue to work with the data pertaining to the Carllson brother’s competition over who is the better Strategema player. For the 100 games they played, besides indicating who was the winner/loser, the duration of the games (in seconds) was also provided. This is variable we will be focusing on for this assignment. Answer or perform the following:

More to Read:

Errors in Reasoning

1) For the games Sven won, provide an estimate of the mean time it takes Sven to beat his brother. Similarly, for the games Jens won, provide an estimate of the mean time it takes for Jens to beat his brother. – 1 pt

2) Construct two QQ-plots, one displaying the durations of the games Sven won, and another displaying the durations of the games Jens won. (Note: When making the QQ-plots, treat them as two separate datasets.) – 2 pt

3) Using the QQ-Plots in part 2, is it plausible to conclude that the distribution of duration for the games Sven won follows a Normal Distribution? Analogously, is it plausible to conclude that the distribution of duration for the games Jens won follows a Normal Distribution? – 1 pts

4) Let S denote the mean duration of games Sven wins. Similarly, let J denote the mean duration of the games Jens wins. Construct a two-sided 70% confidence interval for the quantity, = S – J. Do not assume the standard deviation of the durations are the same for both brother’s wins. – 2 pt

5) Sven won 56 out of the 100 games (see assignment 5 solutions). Based on the prior fact, one might conclude Sven is the better Strategema player. After analyzing the game durations in the previous problems, would you agree with the assessment that Sven is the better player? – 1 pts

Game_Number	Winner	Loser	Duration
1	Jens	Sven	41
2	Sven	Jens	76
3	Sven	Jens	156
4	Sven	Jens	151
5	Sven	Jens	105
6	Jens	Sven	71
7	Sven	Jens	123
8	Sven	Jens	111
9	Sven	Jens	164
10	Sven	Jens	116
11	Jens	Sven	46
12	Sven	Jens	88
13	Jens	Sven	59
14	Jens	Sven	47
15	Jens	Sven	57
16	Sven	Jens	108
17	Sven	Jens	78
18	Sven	Jens	94
19	Jens	Sven	86
20	Jens	Sven	60
21	Jens	Sven	52
22	Jens	Sven	64
23	Jens	Sven	72
24	Jens	Sven	56
25	Jens	Sven	30
26	Sven	Jens	173
27	Jens	Sven	46
28	Jens	Sven	80
29	Sven	Jens	147
30	Jens	Sven	87
31	Jens	Sven	71
32	Sven	Jens	146
33	Sven	Jens	66
34	Jens	Sven	62
35	Jens	Sven	59
36	Sven	Jens	173
37	Jens	Sven	73
38	Jens	Sven	75
39	Sven	Jens	148
40	Jens	Sven	73
41	Sven	Jens	127
42	Sven	Jens	108
43	Jens	Sven	32
44	Jens	Sven	61
45	Jens	Sven	89
46	Jens	Sven	34
47	Jens	Sven	50
48	Jens	Sven	62
49	Sven	Jens	128
50	Sven	Jens	73
51	Sven	Jens	112
52	Sven	Jens	125
53	Sven	Jens	65
54	Sven	Jens	141
55	Sven	Jens	104
56	Sven	Jens	123
57	Jens	Sven	86
58	Jens	Sven	49
59	Sven	Jens	144
60	Sven	Jens	103
61	Jens	Sven	81
62	Sven	Jens	65
63	Jens	Sven	77
64	Jens	Sven	64
65	Sven	Jens	162
66	Sven	Jens	155
67	Sven	Jens	67
68	Sven	Jens	91
69	Jens	Sven	67
70	Sven	Jens	137
71	Jens	Sven	82
72	Jens	Sven	86
73	Sven	Jens	102
74	Sven	Jens	101
75	Sven	Jens	164
76	Jens	Sven	31
77	Sven	Jens	83
78	Sven	Jens	173
79	Sven	Jens	125
80	Jens	Sven	49
81	Sven	Jens	125
82	Sven	Jens	115
83	Jens	Sven	79
84	Jens	Sven	64
85	Sven	Jens	177
86	Sven	Jens	124
87	Jens	Sven	83
88	Sven	Jens	162
89	Sven	Jens	104
90	Sven	Jens	135
91	Sven	Jens	179
92	Jens	Sven	88
93	Jens	Sven	72
94	Sven	Jens	66
95	Sven	Jens	119
96	Sven	Jens	177
97	Jens	Sven	73
98	Sven	Jens	137
99	Sven	Jens	99
100	Sven	Jens	159

Last Updated on March 30, 2021