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 and the relationship between confidence levels, critical values, and the width of confidence intervals.

What is the primary purpose of constructing a confidence interval?

• To determine the sample size

• To calculate the standard deviation

• To find the mean of the sample

• To estimate the population parameter

When the population standard deviation is known, what is used to determine the margin of error?

• Sample mean

• t-distribution

• Population mean

• z_α⁄2 × σ/√n

What does the significance level (α) represent in a confidence interval?

• The sample size

• The probability of the interval not containing the population mean

• The probability of the interval containing the population mean

• The width of the confidence interval

How is the critical value (z_α⁄2) for a 95% confidence interval determined?

• Using the t-distribution

• From the normal tables or software

• By calculating the sample mean

• By dividing the confidence level by two

In a 95% confidence interval, what is the z critical value?

• 1.645

• 1.28

• 2.33

• 1.96

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

• 1.28

• 1.645

• 1.96

• 2.33

What is the margin of error for an 80% confidence interval with a standard deviation of 5.6 and a sample size of 40?

• 1.46

• 1.13

• 2.06

• 1.28

What is the lower limit of the 80% confidence interval if the sample mean is 32?

• 33.13

• 30.87

• 31.54

• 29.94

For a 90% confidence interval, what is the z critical value?

• 1.28

• 1.645

• 2.33

• 1.96

What is the margin of error for a 90% confidence interval with a standard deviation of 5.6 and a sample size of 40?

• 2.06

• 1.46

• 1.28

• 1.13