Please answer the questions below using the book attached about HYPOTHESIS TESTING: CONCEPTS AND TESTS ASSOCIATIONS, MEANS AND PROPORTIONS.

1. Question 1, page 436.

2. Question 3, page 437. *Note that chi-squared must be computed using counts, not percentages.

3. Question 2, page 459. *The critical question is Has the Council proved the point? And, what should the Council recommend. Choose an alpha level and defend your choice.

4. Question 4, page 459.

5. One of my pet peeves is sports commentators who make generalizations without proper use of evidence. In the Qatar Open, recently, Djokovic played Murray in a “two out of three” final match. Djokovic won the first set, and the commentator said, “It may be over. Not only does Djokovic lead Murray 24 to 11, all time, but he’s won 19 of the 20 times when he won the first set. Murray hasn’t been able to come back from that first set loss, when he’s against Djokovic.

So, the commentator was saying that the Djokovic-Murray combination was “special”, different from other pairs of players. With another pair, the player who lost the first set would be at a clear disadvantage, but he would have a chance to come back and win the next two. The commentator was implying that Murray was different and had almost no such chance.

Is 19 and 1 really such strong evidence? I looked up the ATP records in “two out of three” matches. Since 2000, the winner of the first set has won 89% of the matches. (Note that if the players were exactly even, each would have a 50% chance of winning, and we would expect to see the winner of the first set win either of the next two 75% of the time. The losing player would have a 50-50 chance in each set and would have to win both of them, which would happen only 25% of the time.)

So, the average player wins 89% of the matches after winning the first set, and Djokovic has beaten Murray 95% of the time. Now, the question is, are the Djokovic-Murray record and the average record statistically significantly different?