In a poll to estimate presidential popularity, each person in a random sample of

Question

In a poll to estimate presidential popularity, each person in a random sample of 800 voters was asked to agree with one of the following statements:

A total of 620 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 98% confidence interval for the proportion of respondents who feel the president is doing a job. (Round your answers to 2 decimal places.)

Based on your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believes the president is doing a good job?

In a poll to estimate presidential popularity, each person in a random sample of 800 voters was asked to agree with one of the following statements:

Explanation / Answer

a) here sample proportion p=620/800=0.775

for n=800 ; std error =(phat*(1-phat)/n)1/2 =0.0148

for 98% CI ; z=2.3263

therefore 98% confidence interval for the proportion =sample proportion -/+ z*std error

=0.7407 ; 0.8093 ~ 0.74 ; 0.81

b)

as above interval contains proportion all above 0.5 ;

therefore Yes

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