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 the process. The video also discusses how to interpret the results of confidence intervals and highlights the relationship between confidence level, critical value, and margin of error.

What is a confidence interval?

• A single value estimate of a population parameter

• A range of values likely to include a population parameter

• A method to determine the sample size

• A statistical test for hypothesis testing

How is the margin of error calculated when the population standard deviation is known?

• z_α⁄2 × s/√n

• z_α⁄2 × σ/√n

• t_α⁄2 × s/√n

• t_α⁄2 × σ/√n

What is the significance level if the confidence level is 95%?

• 0.05

• 0.95

• 0.025

• 0.975

Where can you find the critical value z_α⁄2?

• In the normal tables or using software

• In the sample data

• In the confidence interval

• In the population data

What is the z-critical value for a 95% confidence level?

• 1.28

• 2.33

• 1.645

• 1.96

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

• 1.96

• 1.28

• 1.645

• 2.33

What is the margin of error for a 90% confidence interval in the example?

• 1.28

• 1.46

• 1.13

• 2.06

What is the lower limit of the 98% confidence interval in the example?

• 30.54

• 29.94

• 30.87

• 32.00

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

• It remains the same

• It becomes more accurate

• It becomes narrower

• It becomes wider

What is the effect of increasing the critical value z on the margin of error?

• Has no effect

• Increases the margin of error

• Makes the margin of error zero

• Decreases the margin of error