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 1,310 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 625 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. (Use Student's t Distribution Table.) (Round your answers to 3 decimal places.)   Confidence interval for the proportion is up to . 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? No Yes

Explanation / Answer

( a )

Confidence Interval for Population Proportion:

P^ (-/+) E

p^ = 625 / 1310 = 0.4771

E = zc * Ö[(p^*(1-p^))/n]

zc is the critical value from normal table for 5% level of significance and we get it as 1.96.

E = 1.96 * Ö((0.4771*(1-0.4771))/1310)

P^ (-/+) E

= 0.4771 (-/+)0.027

= 0.450 and 0.504

Answer:

The 95% confidence interval is (0.450 and 0.504)

( b ) As the upper interval is more than 0.5 for the interval obtained in part (a), so it is reasonable to conclude that majority of the population believes the president is doing a good job.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.