4. The Department of Transportation did a study five years ago that showed that the proportion of cars tested failing to

[answerhappygod]

4. The Department of Transportation did a study five years ago
that showed that the proportion of cars tested failing to meet
pollution control standards was 0.37. In a sample of 100 cars this
year, the proportion not meeting the standards was 0.28. Is there
an overall improvement for the cars to meet the pollution control
standards this year?
a. Formulate the null and alternative hypotheses for the
question.
b. What is the appropriate test probability distribution for the
hypotheses? Explain.
c. Using the 5% significance level to state the decision rule for
the hypotheses.
d. Compute the value of the test statistic.
e. Based on the decision rule in part (c) only, what is the
statistical decision?
f. What conclusion can be drawn in this test?
g. If now we want to construct a two-sided 95% confidence interval
of the population proportion of cars which failed to meet the
standards this year with a margin of error less than or equal to
0.05, is the sample size 100 big enough for this requirement? If
not, how large a sample we should use in order to fulfil this
requirement?