According to a recent survey of 1200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) O Part (b) O Part (c) Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job. O State the confidence interval. (Round your answers to four decimal places.) () Sketch the graph. C.L. = 2
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![According to a recent survey of 1200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job.
**NOTE:** If you are using a Student’s t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
- Part (a)
- Part (b)
- Part (c)
Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.
(i) **State the confidence interval.** (Round your answers to four decimal places.)
[ _______ ] [ _______ ]
(ii) **Sketch the graph.**
The diagram shows a normal distribution curve labeled with:
- \(\frac{\alpha}{2}\) on the left tail and right tail of the curve.
- C.L. = ___ in the center section.
(iii) **Calculate the error bound.** (Round your answer to four decimal places.)
[ _______ ]
### Explanation of Diagram:
The graph depicts a normal distribution curve:
- The curve is centered on the sample proportion \(\hat{P}\).
- The tails represent the \(\alpha/2\) areas, which indicate the significance level split between the two ends of the curve.
- The middle section, marked “C.L.,” represents the confidence level (in this case, 90%).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fbc6c36-d9e9-40b5-b390-5374081e380d%2F50169587-e1d3-40ce-ab21-23a3e9ccb57b%2Fguv8n1a_processed.jpeg&w=3840&q=75)
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