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?
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?
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