Answer:
95% confidence interval for the true percent of NAU students in Flagstaff who love their MAT114 class is (60.77% , 65.23%)
Step-by-step explanation:
Among 1800 NAU students, 1134 students love their class. We have to find the 95% confidence interval of students who love their class.
We will use the concept of confidence interval of population proportion for this problem.
The proportion of students who love the class = p = [tex]\frac{1134}{1800}=0.63[/tex]
Proportion of students who do not love the class = q = 1 - p = 1 - 0.63 = 0.37
Total number of students in the sample = n = 1800
Confidence Level = 95%
The z values associated with this confidence level(as seen from z table) = 1.96
The formula to calculate the confidence interval for population proportion is:
[tex](p-z\times\sqrt{\frac{p \times q}{n}},p+z\times\sqrt{\frac{p \times q}{n}})[/tex]
Using the values in this expression gives:
[tex](0.63-1.96 \times \sqrt{\frac{0.63 \times 0.37}{1800}}, 0.63+1.96 \times \sqrt{\frac{0.63 \times 0.37}{1800}})\\\\ =(0.6077,0.6523)[/tex]
Thus, 95% confidence interval for the true percent of NAU students in Flagstaff who love their MAT114 class is (0.6077 ,0.6523) or (60.77% , 65.23%
