With a perfectly balanced roulette wheel, in the long run, red numbers should tu

Question

With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one casino records the results of 3,800 plays, finding 1890 red numbers. Is that too many reds? Or chance variation?
a. Formulate the null and alternative hypothesis as statements about a box model.
b. The null says that the percentage of reds in the box is ___. The alternative says that the percentage of reds in the box is _ __. Fill in the blanks.
c. Compute z and P
d. Were there too many reds?

Explanation / Answer

a)Ho := 18/38= 0.474

Ha: >0.474

P(hat)= 1890/3800= 0.497

b) equal to 18/38; Greater than 18/38

c) z= (.497-.474)/.474(1-.474)/3800= (.497-.474)/.0081= 2.84

P value (from normal curve table)=.0023

d) Looks like there were too many reds as the probability of this happening by chance was only .0023.

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