Question 1160295: Car brands Toros and Sahin are guaranteed for 1 year. In a random sample of 50 cars of brand Toros, 12 were observed to fail before the guarantee period ended. An independent random sample of 60 brand Sahin cars also revealed 12 failures during the guarantee period.
a) Estimate the true difference (Toros-Sahin) between proportions of failures during the guarantee period, with 98% confidence interval. Explain which brand has a better quality.
b) For car brand Toros, test, at the 5% level, the hypothesis that exactly 25% of all Toros cars population would fail before the guarantee period ended.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The true difference is in the interval (-0.1449,+ 0.2249), which means there could have been anywhere from a 14% difference favoring Toros and 22% difference favoring Sahin. Since 0 is in the interval, one cannot say that there is a true difference between the two. The samples have a difference, but one could have seen this difference by chance.
Ho: u=0.25
Ha:u NE 0.25
alpha=0.05 p(reject Ho|Ho true)
z with critical value 1.96
z=(p hat-p)/sqrt(p*(1-p)/n)
=(.24-.25)/sqrt(.25*.75/50)
=-.01/.06=-0.167
fail to reject Ho. Exactly 25% of cars could fail before the period ended.
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