On June 2, 2010, major league pitcher Armando Galarraga of the Detroit Tigers lo

Question

On June 2, 2010, major league pitcher Armando Galarraga of the Detroit Tigers lost his bid for a perfect game when umpire Jim Joyce incorrectly called a runner safe at first base with two outs in the ninth inning (A perfect game occurs when a pitcher faces 27 batters without any opposing players reaching base during the game Only 18 perfect games have been pitched in the last 110 years of baseball.) This unfortunate incident led to an outcry for baseball to expand its use of instant replay so that umpires have the option of reversing incorrect calls A USA Today/Gallup poll after this event found that 78% of baseball fans were in favor of expanding the use of instant replay in Major League Baseball Suppose the size of this sample was 600 people. a. Estimate the true proportion of baseball fans in favor of expensed replay using a 95% confidence interval b. What is the margin of error for this sample? c. Verify your result using PHStat

Explanation / Answer

Part-a

95% confidence intevral =0.78-1.96*sqrt(0.78*(1-0.78)/600) , 0.78+1.96*sqrt(0.78*(1-0.78)/600)

=(0.746853392       0.813146608)

Part-b

Margin of error=1.96*sqrt(0.78*(1-0.78)/600) =0.0332

Part-c

Confidence Interval Estimate for the Mean Data Sample Size 600 Number of Successes 468 Confidence Level 95% Intermediate Calculations Sample Proportion 0.78 Z Value -1.95996398 Standard Error of the Proportion 0.016911535 Interval Half Width 0.033145999 Confidence Interval Interval Lower Limit 0.746854001 Interval Upper Limit 0.813145999

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