I have work for all of them but I just want to reconfirm my thoughts with a tutor. Suppose you are a casino owner, and your casino runs a very simple...

I have work for all of them but I just want to reconfirm my thoughts with a tutor.

Question 1.

A certain customer plays the game 20 times and wins 13 of the bets. You suspect that the customer is cheating! That is, you think that their chance of winning is higher than the normal chance of winning.

You decide to test your hunch using the outcomes of the 20 games you observed.

Question 2. Define the null hypothesis and alternative hypothesis for this investigation.

Question 3. Given the outcome of 20 games, which of the following test statistics would be a reasonable choice for this hypothesis test?

Hint: For a refresher on choosing test statistics, check out Section 11.3 of the textbook.

1. Whether there is at least one win.
2. Whether there is at least one loss.
3. The number of wins.
4. The number of wins minus the number of losses.
5. The total variation distance between the probability distribution of a fair coin and the observed distribution of heads and tails.
6. The total amount of money that the customer won.

Assign reasonable_test_statistics to a list of numbers corresponding to these test statistics.

Question 4. simulate

Question 5.test_statistics_under_null

Question 6.

Question 7. Compute an empirical P-value for this test.

Hint: Which values of our test statistic are in the direction of the alternative hypothesis?

Question 8.

Question 9.p_value

Question 10.

Question 11.