Question

A random sample of 1800 NAU students in Flagstaff found 1134 NAU students who love their MAT114 class. Find a 95% confidence interval for the true percent of NAU students in Flagstaff who love their MAT114 class. Express your results to the nearest hundredth of a percent. .

Answer 1

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 = $\frac{1134}{1800}=0.63$

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:

$(p-z\times\sqrt{\frac{p \times q}{n}},p+z\times\sqrt{\frac{p \times q}{n}})$

Using the values in this expression gives:

$(0.63-1.96 \times \sqrt{\frac{0.63 \times 0.37}{1800}}, 0.63+1.96 \times \sqrt{\frac{0.63 \times 0.37}{1800}})\\\\ =(0.6077,0.6523)$

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%