A sample of 1200 Freshmen at UGA were asked if they had applied for student foot

Question

A sample of 1200 Freshmen at UGA were asked if they had applied for student football tickets. The proportion who answered yes was 0.88. The standard error of this estimate is 0.009.

(a) Find the margin of error for a 95% confidence interval for the population proportion who applied for football tickets.
(3 decimal places)

(b) Construct the 95% confidence interval.

(c) If the sample was randomly selected, will this confidence interval be valid?

Yes because both (1200)*(0.88) and (1200)*(1 - 0.88) are greater than 15.Yes because the sample size is greater than 30.     None of these.Yes because at least one of (1200)*(0.88) and (1200)*(1 - 0.88) is greater than 15.Yes because at least one of (1200)*(0.88) and (1200)*(1 - 0.88) is greater than 30.

(d) Using the above confidence interval, what can you say about the true population proportion?

If we were to take many samples like this, and calculate a 95% confidence interval for each one, approximately 95% of these intervals would contain the true population proportion.We are 95% confident that the sample proportion is in this interval.   

Explanation / Answer

Here p=0.88 and n=1200 and SE=0.009

a. Margin of Error=z*SE=1.96*0.009=0.018

b. CI=p+/-E=0.88+/-0.018=(0.862,0.898)

c. Yes because n>30

d. approximately 95% of these intervals would contain the true population proportion.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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