Stats Assignment 11
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School
Rutgers University *
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Course
01:960:285
Subject
Statistics
Date
Jan 9, 2024
Type
Pages
1
Uploaded by CountElectron9465
Amaya Lowe
Professor Andrew Magyar
Intro to Stats for Business
2023 December 10
Strategema is the latest craze in the gaming world. In the game of Strategema, two players
compete until a victor is determined, there can be no draws.
Two brothers, Sven and Jens Carlsson have a friendly sibling rivalry going. To decide
bragging rights, the two brothers play 100 games of Strategema to settle who is the better
player.
The attached dataset contains data from the 100 games the Carlson brothers played. The
The fields included are the game number, the winner, the loser, and the duration of the
game (in seconds).
1) Provide an estimate of the probability that Sven wins.
a)
Probability =
. This means that Sven probably won around 56% of
56
100
= 0. 56 = 56%
the games that they played.
2) Construct an 80% two-sided confidence interval for the probability Sven wins.
a)
To construct an 80% two-sided confidence interval, we first need to find the Standard
Error.
b)
Standard Error =
. Now that we know the Standard
0. 56 × 0. 44 ÷ 100
= 0. 0496
error, we can plug it into the confidence interval equation.
c)
80% CI =
0. 56 ± 1. 282 × 0. 0496
d)
Lower Bound =
0. 56 − 1. 282 × 0. 0496 = 0. 56 − 0. 0635872 = 0. 4964128
e)
Upper Bound =
0. 56 + 1. 282 × 0. 0496 = 0. 56 + 0. 0635872 = 0. 6235872
f)
This means that the 80% Confidence Interval is (0.4964, 0.6236)
3) What is the margin of error for the confidence interval calculated in Part 2?
a)
The Margin of Error for the confidence interval is
0. 5 × (0. 6236 − 0. 4964) =
0. 0636
4) How many games would the Carlson brothers need to play to obtain a 90% two--
sided confidence interval for the probability Sven wins that has a margin of error of
0.05?
a)
The Carlson brothers would need to play 267 games.
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