Stats Assignment 11

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Rutgers University *

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01:960:285

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Statistics

Date

Jan 9, 2024

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pdf

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1

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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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