In a simple random sample of 70 automobiles registered in a certain state, 28 of them were found to have emission levels that exceed a state standard.
a. What proportion of the automobiles in the sample had emission levels that exceed the standard?
b. Find a 95% confidence interval for the proportion of automobiles in the state whose emission levels exceed the standard.
c. Find a 98% confidence interval for the proportion of automobiles whose emission levels exceed the standard.
d. How many automobiles must be sampled to specify the proportion that exceed the standard to within ±0.10 with 95% confidence?
e. How many automobiles must be sampled to specify the proportion that exceed the standard to within ±0.10 with 98% confidence?
f. Someone claims that less than half of the automobiles in the state exceed the standard. With what level of confidence can this statement be made?