Question

Ava likes playing soccer, specifically shooting free kicks. She practices by shooting the ball 30 meters away from the goal and always scores if she places the ball in the top right quadrant of the goal (where the goalkeeper can’t reach it) and misses if she places it elsewhere. Her data is the following, where (X) means she didn’t score and (O) means she scored: O O X X X X O O X X O O O X X X X X O O X X X X O O O X X X

1. What is the conditional probability of a score following a score?

a. 7/12

b. 12/30

c. 2/7

d. None of the above.

2. What is the conditional probability of a score following two scores?

a. 7/13

b. 17/30

c. 2/7

d. None of the above.

3. What is the number of runs?

a. 10

b. 11

c. 12

d. 13

4. Suppose we perform a runs test, and find that Ava's expected number of runs is 15.4 and the z-statistic associated with her actual number of runs is -2.09. At a 5% significance level, which of the following is true?

a. We cannot say anything about Ava's performance as a p-value is not provided.

b. Ava's number of runs is significantly less than her expected number of runs.

c. Ava's number of runs is significantly greater than her expected number of runs.

d. Ava's number of runs is not significantly different from her expected number of runs.

5. On the basis of the Runs test, we can say that Ava has a hot hand.
a. True
b. False

Answer 1