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 1,470 voters was asked to agree with one of the following statements:

A total of 575 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 90% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use Student's t Distribution Table.) (Round your answers to 3 decimal places.)

Based on your interval in part (a), is it reasonable to conclude that a majority 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 1,470 voters was asked to agree with one of the following statements:

Explanation / Answer

Sample size : n = 1470 sufficient enough to follow the standard normal distribution

575 said he is doing a good job.

575 / 1470 = 39.11%

Hypothesis testing

Ho : Majority thinks he is doing a good job ( p >= 0.5 )

Ha: Majority doesn’t think that way ( p < 0.5 )

Majority here means more than 50% that means 735. So we have to check whether we have sufficient data to reject the null hypothesis Ho or not.

sd= p x (1-p) where p is the probability of success

90 % Confidence interval signifies

= 0.5 +_ SE * Z

SE = Standard error = (Std. dev) / Sqrt(n) where n is the sample size and Z is the statistic value for 90% confidence interval which is 1.65 ( using z table)

SE = sqrt( 0.5 * (1 - 0.5) /1470)

So our interval is [ 0.5+ (0.013*1.65) , 0.5 - (0.013*1.65) ] which is [0.52145 , 0.47855]

This was just the proportion so converting it by multiplying by 1470 gives [ 704 , 767]

So we can reject our null hypothesis and can say that he is not doing a good job

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