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In a simple random sample of 70 automobiles registered in a certain state, 28 of them
Chapter 5, Problem 1(choose chapter or problem)
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 \(\pm 0.10\) with \(95 \%\) confidence?
(e) How many automobiles must be sampled to specify the proportion that exceed the standard to within \(\pm 0.10\) 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?
Equation Transcription:
Text Transcription:
95%
98%
\pm 0.10
95%
\pm 0.10
98%
Questions & Answers
QUESTION:
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 \(\pm 0.10\) with \(95 \%\) confidence?
(e) How many automobiles must be sampled to specify the proportion that exceed the standard to within \(\pm 0.10\) 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?
Equation Transcription:
Text Transcription:
95%
98%
\pm 0.10
95%
\pm 0.10
98%
ANSWER:
Problem 5.2.1
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?
Step by Step Solution
Step 1 of 6
In a sample of 70 automobiles registered in a certain state, 28 of them were found to have emission rates that exceed a state standard.
To determine what proportion of the automobiles in the sample had emission levels that exceed the standard
Here, the number of successes is 28 and the given sample size is 70
Therefore, the required proportion is
To find a 95% confidence interval for the proportion of automobiles in the state whose emission level exceeds the standard
Here, . Therefore,
The number of success is. Then,