Research in the gaming industry showed that 10% of all slot machines in the Unit

Question

Research in the gaming industry showed that 10% of all slot machines in the United States stop working each year. Short’s Game Arcade has 60 slot machines and only 3 failed last year. At the .05 significance level, test whether these data contradict the research report.

State the null and alternate hypotheses.

Evaluate the test statistic. (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places.)

Make the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

What is the p-value? (Round your answer to 4 decimal places.)

What does p-value imply?

Research in the gaming industry showed that 10% of all slot machines in the United States stop working each year. Short’s Game Arcade has 60 slot machines and only 3 failed last year. At the .05 significance level, test whether these data contradict the research report.

Explanation / Answer

Part-b

H0:=0.10

H1:0.10

Part-c-1

Sample proportion phat=3/60=1/20=0.05

Sample size n=60

Test statistic Z=(phat-0.10)/sqrt(0.10*(1-0.10)/n)

=(0.05-0.10)/sqrt(0.10*(1-0.10)/60)

=-1.29

Part-c-2

Reject Ho if Z is not between -1.960 and 1.960

Part-d-1

p-value=2*P(Z<-1.29)=0.1971

Part-d-2

p-value does not shows a different failure rate at Short’s slots

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