In the state of Louisiana, a random sample of 150 legally-registered automobiles

In the state of Louisiana, a random sample of 150 legally-registered automobiles was recently taken. Of the 150, only 74 passed the state's emission test for pollution.

(a) Find a point estimate of the true proportion of the automobiles in Louisiana that passed the emission test for pollution.

(b) Find a 90% confidence interval for the proportion of automobiles in Louisiana that passed the emission test for pollution.

(c) Olivier Giroud, an environmental engineer, would like to design a larger study to estimate the population proportion. He would like to write a 95% confidence interval that will have margin of error equal to 0.02. How many cars will he need to sample?

(d) Hugo Lloris, another engineer, exclaims “What! Olivier, that's a lot of cars! I don't think we have the money or resources to make this happen! Is there a way to keep the 95 percent confidence level but have a smaller number of cars for the study?”. Discuss briefly, one way Olivier could reduce the number of cars needed. Hint: You may find sample size (n) formula on page 6 of lecture 12, useful.