question archive A gasoline lawn mover manufacturer claims that their power lawn movers start up on the first try 95% of the time

A gasoline lawn mover manufacturer claims that their power lawn movers start up on the first try 95% of the time

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A gasoline lawn mover manufacturer claims that their power lawn movers start up on the first try 95% of the time. A consumer's protection group feels the manufacturer claim is too high and randomly selects 200 of the manufacturer's movers and finds that 184 start up on the first try. Would this indicate the manufacturer was indeed exaggerating at a=1%?

 

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The standard error is sqrt(0.95*0.05/200) = 0.0154. Thus the test statistic of the observed proportion of 0.92 is (0.92-0.95)/0.0154 = -1.948. This is a one-tailed test since we are only looking for exaggeration, so the critical one-tail value at the 0.01 level is -2.326. Since the magnitude of this is not larger than that magnitude, we cannot conclude that the claim is exaggerated.

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