n a poll to estimate presidential popularity, each person in a random sample of
ID: 1166304 • Letter: N
Question
n a poll to estimate presidential popularity, each person in a random sample of 1,150 voters was asked to agree with one of the following statements:
1. The president is doing a good job.
2. The president is doing a poor job.
3. I have no opinion.
A total of 550 respondents selected the first statement, indicating they thought the president was doing a good job.
a. Construct a 95% confidence interval for the proportion of respondents who feel the president is doing a good job. round to 3 decimal places
b. 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?
Explanation / Answer
SOLUTION OF (a)
Since it is a discrete binary data so Adjusted Wald technique can be used to find confidence interval:
a. Multiply the adjusted proportion by (1 – the adjusted proportion).
0.478(1-0.478)= 0.249
b. Divide this result by the adjusted sample size from step 2.
0.249/ 1154 = 0.00022
c. Take the square root of the value from step b.
0.00022=0.0148
4.Compute the margin of error by multiplying the standard error (result from step 3c) by 2.
0.0148×2=0.0297
5.Compute the confidence interval by adding the margin of error from the sample proportion from step 2 and then subtracting the margin of error from the sample proportion.
0.479+.0.0297=0.509
0.479-.0.0297=0.4493
The 95% confidence interval is 0.449 to 0.509. Our best estimate of the entire customer population’s intent to repurchase is between 44.9% to 50.9%. .
SOLUTION OF (b)
Based on the result in part (a) it can’t be concluded that majority a majority of the population believes the president is doing a good job.
Note: I’ve rounded the values to keep the steps simple. If you want more a more precise confidence interval, use the online calculator.
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