SOLUTION: The Department of Transportation 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 st

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Question 1194200: The Department of Transportation 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 than they used to be? Clearly state the null and
alternative hypotheses. Perform the hypothesis 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: p is 0.37
Ha: the proportion not meeting the standard is unchanged or p NE 0.37
alpha=0.01 p{reject Ho|Ho true}
test is a 1 sample p
critical value is |z|>2.576
z=(phat-0.37)/sqrt(0.37*0.63/100)
=-0.09/0.0482=-1.86
fail to reject Ho with insufficient evidence to say that there was a change
99% half-interval is 2.576*SE, which Is sqrt(0.28*0.72/100)=0.0449
half-interval is 0.1157
(0.16, 0.40) Because 0.37 is in the interval of uncertainty there is insufficient evidence to say that there has been a significant change at the 99% level.