Sara loves to bowl. She never has an open frame; each frame is either a strike (

Question

Sara loves to bowl. She never has an open frame; each frame is either a strike (X) or a spare (/). Here is a list of her data in the past three games: xxxx////x////xxxxxx////xxx//xxxxx///xx a. What is the probability that Sara rolls a strike on a given frame in this sample? b. What is the probability that Sara rolls a strike in a frame following a strike? c. How many runs does Sara have? d. Go to the following website: http://www.quantitativeskills.com/sisa/statistics/ordinal.htm and perform the runs test. i. In the box marked "N group 1" enter the number of strikes. ii. In the box marked "N group 2" enter the number of spares. iii. In the box marked "Number of Runs" enter your answer to part c. How many runs were expected? What is the z-value for this test? Does the test show evidence of the hot hand? e. Draw a picture of the distribution of the number of runs, and show where Sara's number of runs falls on this distribution (i.e. the location of z-statistics). You can copy the picture from page 15 of the Hot Hand slides if that is easier.

Explanation / Answer

Answer:

(A) Total number of shots = 38

Number of strikes = 21

Probability of strike = 21 / 38 = 0.55

Thus Probability of spare = 1 - 0.55 = 0.45

(B) To find the probability of hitting strike following a strike.

probability of hitting strike following a strike = 12/38 = 0.315

(C) Number of runs = 11 (count the number of observations coming together. the observations coming together is counted as one.)

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