Confidence Intervals and Sample Size Effects

This video tutorial explains how to construct confidence intervals for a population mean using the Student t-distribution. It covers the concept of confidence intervals, the properties of the t-distribution, and how to use the t-distribution table to find critical values. The video includes examples of constructing confidence intervals for both small and large sample sizes, highlighting the impact of sample size on the margin of error and the width of the confidence interval.

What is the primary purpose of constructing a confidence interval?

• To determine the sample size

• To calculate the standard deviation

• To find the exact population mean

• To estimate the range in which the population mean likely falls

Which distribution is used when the population standard deviation is unknown?

• Binomial distribution

• Poisson distribution

• t-distribution

• Normal distribution

What is the shape of the t-distribution compared to the standard normal distribution?

• Flatter and wider

• Identical

• Narrower and taller

• Skewed to the right

What determines the shape of each t-distribution?

• Significance level

• Sample mean

• Degrees of freedom

• Confidence level

Where can you find the critical values for the t-distribution?

• In the Z-distribution table

• At the top of the t-distribution table

• In the appendix of a statistics textbook

• In the body of the t-distribution table

What is the significance level for a 90% confidence interval?

• 0.05

• 0.10

• 0.90

• 0.95

For a sample size of 12, what are the degrees of freedom?

• 10

• 13

• 12

• 11

What is the critical value for a 95% confidence interval with 14 degrees of freedom?

• 1.960

• 2.145

• 1.796

• 2.639

In the example with a sample size of 15, what is the margin of error?

• 1.94

• 2.00

• 1.50

• 2.50

What is the lower limit of the confidence interval in the example with a sample size of 15?

• 21.94

• 20.00

• 19.00

• 18.06