Confidence Intervals and Critical Values

This video tutorial explains how to construct confidence intervals for a population mean when the population standard deviation is known. It covers the concept of confidence intervals, the calculation of margin of error using critical values, and provides an example using exam scores to demonstrate confidence interval calculations at different confidence levels. The video concludes with an interpretation of the results, highlighting how confidence levels affect the width of the confidence interval.

What is a confidence interval used for in statistics?

• To find the standard deviation of a population

• To calculate the mean of a sample

• To estimate a range of values likely to include a population parameter

• To determine the exact value of a population parameter

If the confidence level is 95%, what is the significance level (α)?

• 0.95

• 0.10

• 0.05

• 0.025

What is the critical value (z_α/2) for a 95% confidence interval?

• 1.28

• 1.645

• 1.96

• 2.33

For an 80% confidence interval, what is the z-critical value?

• 1.645

• 1.96

• 2.33

• 1.28

What is the margin of error for a 90% confidence interval with a z-critical value of 1.645?

• 1.13

• 1.46

• 2.06

• 1.28

What is the lower limit of the 80% confidence interval if the sample mean is 32 and the margin of error is 1.13?

• 31.87

• 33.87

• 32.87

• 30.87

For a 98% confidence interval, what is the z-critical value?

• 1.96

• 2.33

• 1.645

• 1.28

What is the upper limit of the 90% confidence interval if the sample mean is 32 and the margin of error is 1.46?

• 30.46

• 31.46

• 32.46

• 33.46

How does the margin of error change as the confidence level increases?

• It becomes zero

• It increases

• It remains the same

• It decreases

What happens to the width of the confidence interval as the confidence level increases?

• It widens

• It becomes zero

• It narrows

• It remains unchanged