A basketball player took 35 free throws during the season. Her sequence of hits

Question

A basketball player took 35 free throws during the season. Her sequence of hits (H) and misses (M) is shown. At alpha = .01. is her hit/miss sequence random? H M M H H M H M M H H H H H M M H H M M H M H H H M H H H H M M M H H (a) The correct null and alternative hypotheses are a. H_0: Events follow a random pattern H_1. Events do not follow a random pattern b. H_0: Events do not follow a random pattern H_1. Events follow a random pattern a b (b) Calculate the expected number of runs. (Round your answer to 3 decimal places.) Expected value (c) Calculate the z-score and the p-value (A negative value should be indicated by a minus sign. Round your answers to 4 decimal places. Use the formulas in the textbook to determine the z-score, not Mega Stat. Use Excel to calculate the p-value.) z-score p-value

Explanation / Answer

(a) Answer of this question is option a) i.e.

H0:Events follow random pattern

H1:Events do not follow random pattern

(b) Let us first define run. A run is defined as a series of consecutive positive (or negative) values.

Let R is the observed number of runs=17

Also, n1 and n2 denoting the number of positive(H) and negative(M) values in the series.

Here, n1=21

n2=14

By defination, expected number of runs is,

E(R)=((2*n1*n2)/(n1+n2))+1

=((2*21*14)/(21+14))+1

=17.8

(c) The test statistic for testing above hypothesis is,

Z0=(R?E(R)/sR

where R is the observed number of runs, E(R), is the expected number of runs, and sR is the standard deviation of the number of runs. The value sR is computed as follows:

s2R=[2n1n2(2n1n2?n1?n2)]/[(n1+n2)2(n1+n2?1)]

=[2*21*14(2*21*14?21?14)]/[(21+14)2(21+14?1)]

=7.807059

Z-score is,

Z0=(R?E(R)/sR

   =(17-17.8) / 2.794111

=-0.2863

p-value=P(Z>|Z0|)=P(Z<0.2863 or Z>0.2863)=0.7746 ,where Z~N(0,1)

Conclusion: Since p-value >0.05 , we accept H0 at 5% level of significance.

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