SOLUTION: 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

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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.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Ho: proportion=0.37
Ha: proportion NE 0.37
alpha=0.01 p{reject Ho|Ho true}
test is a z
critical value |z|> 2.576
z=(0.28-0.37)/sqrt(0.37*0.63/100)
=-0.09/0.0483
=-1.86
fail to reject Ho: there is insufficient evidence to reject the null hypothesis at the 1% level.
half-interval is (0.995)z*SE=0.1244
99% Interval is (0.246, 0.494)
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.