Confidence Intervals and Z-Scores

This lesson explains how to calculate a confidence interval for an unknown population mean with a known population standard deviation. It covers the steps of calculating the sample mean, finding the z-score for the confidence level, calculating the error bound, and constructing the confidence interval. An example problem is provided, demonstrating the process using a sample of exam scores. The video also shows how to find the z-score using a TI-84 calculator and Desmos. Finally, it interprets the confidence interval in the context of the problem.

What is the first step in calculating a confidence interval for an unknown population mean?

• Find the z-score

• Calculate the sample mean

• Determine the error bound

• Interpret the confidence interval

In the example problem, what is the given population standard deviation?

• 5 points

• 4 points

• 3 points

• 2 points

What is the confidence level used in the example problem?

• 95%

• 90%

• 85%

• 80%

How is the z-score for a 90% confidence level found using a TI-84 calculator?

• Using the normalcdf function

• Using the poissonpdf function

• Using the invNorm function

• Using the binomcdf function

What is the approximate z-score for a 90% confidence level?

• 1.645

• 1.282

• 1.960

• 2.576

What is the formula for calculating the error bound?

• Population standard deviation times sample size

• Z-score times population standard deviation divided by square root of sample size

• Sample mean divided by z-score

• Z-score times sample mean

What is the confidence interval calculated in the example problem?

• 68.0 to 69.0

• 66.5 to 69.5

• 67.0 to 68.0

• 67.5065 to 68.4935

What does the confidence interval represent in the context of the example problem?

• The range of possible sample means

• The range of possible z-scores

• The range of possible standard deviations

• The range of possible population means

What is the final step in the confidence interval calculation process?

• Determine the error bound

• Calculate the sample mean

• Find the z-score

• Interpret the confidence interval

What additional resource is mentioned at the end of the lesson?

• A table of z-scores for specific confidence levels

• A guide to using the TI-84 calculator

• A chart of population standard deviations

• A list of sample means