According to a recent survey of 1500 people, 64% 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 acceptab 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) In words, define the random variables X and P. O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job. O Xis the proportion of people in the sample who feel the president is doing an acceptable job, and Pis the number of people who feel the president is doing an acceptable job. O X is the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job. O Yis the pumber of people u

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According to a recent survey of 1500 people, 64% 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)
In words, define the random variables X and P'.
O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job.
O Xis the proportion of people in the sample who feel the president
sdoing an acceptable job, and P' is the number of people who feel the president is doing an acceptable job.
O Xis the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job.
O Xis the number of people who feel the president
doing an acceptable job, and P' is the proportion
people in the sample who feel the president is doing an acceptable job.
O Part (b)
Which distribution should you use for this problem? (Round your answers to four decimal places.)
P'-
Explain your choice.
O The standard normal distribution should be used because V npg z 10, which implies a large sample.
O The standard normal distribution should be used because we are interested in proportions and the sample size is large.
O 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."
O The Student's t-distribution should be used because we do not know the standard deviation.
Transcribed Image Text:According to a recent survey of 1500 people, 64% 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) In words, define the random variables X and P'. O Xis the number of people who feel the president is not doing an acceptable job, and P'is the proportion of people in the sample who feel the president is not doing an acceptable job. O Xis the proportion of people in the sample who feel the president sdoing an acceptable job, and P' is the number of people who feel the president is doing an acceptable job. O Xis the proportion of people in the sample who feel the president is not doing an acceptable job, and P'is the number of people who feel the president is not doing an acceptable job. O Xis the number of people who feel the president doing an acceptable job, and P' is the proportion people in the sample who feel the president is doing an acceptable job. O Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) P'- Explain your choice. O The standard normal distribution should be used because V npg z 10, which implies a large sample. O The standard normal distribution should be used because we are interested in proportions and the sample size is large. O 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." O The Student's t-distribution should be used because we do not know the standard deviation.
OPart (c)
Constrlict 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. =
%3D
P'
(iii) Calculate the error bound. (Round your answer to four decimal places.)
8|N
Transcribed Image Text:OPart (c) Constrlict 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. = %3D P' (iii) Calculate the error bound. (Round your answer to four decimal places.) 8|N
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