53, The National Center for Education Statistics reported that 47% of college st

Question

53, The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study. a. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. what happens to the margin of error as the confidence is increased from 95% to 99%? b. c,

Explanation / Answer

Solution(a)
Given in the question
Population proportion = 0.47
No. of sample = 450
at 95% confidence level, alpha = 0.05 and alpha/2 = 0.025
Where Zalpha/2 or Z0.025 = 1.96
So confidence interval can be calculaed as follows:
0.47 - 1.96*sqrt(0.47*(1-0.47)/450)) to 0.47 + 1.96*sqrt(0.47*(1-0.47)/450))
0.47-1.96*sqrt(0.00055355) to 0.47+1.96*sqrt(0.00055355)

0.47 -1.96*0.0235 to 0.47 + 1.96*0.0235
0.47-0.04606 to 0.47+0.04606
0.42394 to 0.51606
So 95% confidence interval is 0.42394 to 0.51606
Solution(b)
99% confidence interval can be calculated as follows:
alpha = 0.01 and alpha/2= 0.005 so Zalpha/2 or Z0.005 is 2.5758
So confidence interval can be calculated as
0.47 -2.5758*0.0235 to 0.47 + 2.5758*0.0235
0.47 - 0.0605313 to 0.47 + 0.0605313
So confidence interval is 0.4094687 to 0.5305313

Solution(c)
As we can see that at 95% confidence interval margin of error is
1.96*sqrt(0.47*(1-0.47)/450)) = 0.04606
And at 99% confidence interval margin of error is 2.5758*sqrt(0.47*(1-0.47)/450)) = 0.06053

Here we can see that as confidence interval increased margin of error also increased.

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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