Confidence Interval Calculations

The video tutorial explains how to construct a 95% confidence interval for the true population proportion of college freshmen returning to college the next year. It uses a sample from 2004, where 1,221 out of 1,650 freshmen returned. The tutorial details the formula for the confidence interval, including calculating p-hat and q-hat, and simplifying the formula to find the lower and upper bounds. The result shows a 95% confidence that the true proportion is between 0.719 and 0.761.

What year did the ACT report the sample data used in the example?

• 2000

• 2004

• 2010

• 2015

How many college freshmen were in the sample?

• 1,500

• 2,000

• 1,221

• 1,650

What is the formula used to construct a confidence interval for the true population proportion?

• p-hat ± t * sqrt(q-hat / n)

• p-hat ± z * sqrt(p-hat / n)

• p-hat ± t * sqrt(p-hat * q-hat / n)

• p-hat ± z * sqrt(p-hat * q-hat / n)

What is the value of p-hat in the given example?

• 0.80

• 0.50

• 0.26

• 0.74

How is q-hat calculated?

• 1 - p-hat

• 1 - n

• 1 - z

• 1 - x

What is the value of q-hat in this example?

• 0.50

• 0.80

• 0.26

• 0.74

What is the z-value used for a 95% confidence interval?

• 1.64

• 2.33

• 1.96

• 2.58

What is the calculated error term in this example?

• 0.0108

• 0.015

• 0.021

• 0.030

How is the lower bound of the confidence interval calculated?

• p-hat + error

• p-hat - error

• q-hat - error

• q-hat + error

What is the lower bound of the confidence interval in this example?

• 0.700

• 0.719

• 0.740

• 0.761