STAT 212 – Assignment 5

Due Date: March 24th, 2021

Data Description and Background

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 finally settle who is the better player.

The attached dataset contains data from the 100 games the Carllson brothers played. The fields included are the game number, the winner, the loser and the time duration of the game (in seconds).

1) Provide an estimate of the probability that Sven wins. – ½ pt

2) Construct an 80% two-sided confidence interval for the probability Sven wins. – 1 pt

3) What is the margin of error for the confidence interval calculated in Part 2? – ½ pts

4) Let the parameter p be the probability Sven wins. Frame their competition as a hypothesis testing problem where the null is that they are evenly matched versus the alternative that one is better than the other (i.e. explicitly write out the null and alternative hypothesis in terms of p). – 1 pt

5) The Carllson brothers are extremely competitive and want to be nearly certain they can determine if they are evenly matched, or one is better at Strategema. In the event they are in fact evenly matched, they wish to be 99% certain they do not erroneously declare one brother the superior player. However, in the event one brother is in fact slightly better (assume his probability of winning is 0.51), they want to be able to detect it 99% of the time. Is 100 games enough, or do they need to play more? If the latter, how many games should they play? – 1 pt