document.write( "Question 1185791: The Department of Transport in South Africa conducted a study a number of years ago that showed that the proportion of cars tested which failed to meet the state pollution standard was 37%. The department would like to be able to say that the cars have improved since then. In a sample of 100 cars more recently, the proportion not meeting the standards was 28%. Are the cars better at meeting the standards that they used to be? Clearly state the null and alternative hypothesis. Perform the hypothesis test test at 99% confidence level and explain the meaning of your conclusion. \n" ); document.write( "

Algebra.Com's Answer #816625 by Boreal(15235) $\"\"$ $\"About$

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Ho: proportion=0.37
\n" ); document.write( "Ha: proportion NE 0.37
\n" ); document.write( "alpha=0.01 p{reject Ho|Ho true}
\n" ); document.write( "test is a z
\n" ); document.write( "critical value |z|> 2.576
\n" ); document.write( "z=(0.28-0.37)/sqrt(0.37*0.63/100)
\n" ); document.write( "=-0.09/0.0483
\n" ); document.write( "=-1.86
\n" ); document.write( "fail to reject Ho: there is insufficient evidence to reject the null hypothesis at the 1% level.
\n" ); document.write( "half-interval is (0.995)z*SE=0.1244
\n" ); document.write( "99% Interval is (0.246, 0.494)
\n" ); document.write( "Because 0.28 is in the interval, we fail to reject Ho. The percentage could be 0.28 with a true percentage of 0.37 and 100 vehicles sampled.
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