According to a recent survey of 1400 people, 65% 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.) Please label each part

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According to a recent survey of 1400 people, 65% 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.)

Please label each part

Part (b)
Which distribution should you use for this problem? (Round your answers to four decimal places.)
P'-
Explain your choice.
The binomial distribution should be used because the two outcomes are "the president is doing a good job" and "the president is not doing a good job."
The Student's t-distribution should be used because we do not know the standard deviation.
The standard normal distribution should be used because we are interested in proportions and the sample size is large.
The standard normal distribution should be used because
npq 2 10, which implies a large sample.
Correct! We use the standard normal distribution to create confidence intervals about the population proportion.
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.
C.L. =
2
2
P'
(iii) Calculate the error bound. (Round your answer to four decimal places.)
II
Transcribed Image Text:Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) P'- Explain your choice. The binomial distribution should be used because the two outcomes are "the president is doing a good job" and "the president is not doing a good job." The Student's t-distribution should be used because we do not know the standard deviation. The standard normal distribution should be used because we are interested in proportions and the sample size is large. The standard normal distribution should be used because npq 2 10, which implies a large sample. Correct! We use the standard normal distribution to create confidence intervals about the population proportion. 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. C.L. = 2 2 P' (iii) Calculate the error bound. (Round your answer to four decimal places.) II
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