Sample Size and Confidence Intervals

This lesson explains how to determine the sample size needed for a confidence interval of a population mean. It uses a scenario where you estimate how much parents spend on their kids' birthday parties. Given a population standard deviation of $20.3 and a desired confidence level of 95%, the lesson guides you through finding the Z-score and using a formula to calculate the sample size. The process involves using a graphing calculator to find the Z-score and applying the sample size formula. The final sample size is rounded up to ensure accuracy.

What is the main objective of this lesson?

• To learn how to calculate the mean of a population.

• To determine the sample size needed for a confidence interval.

• To understand the concept of standard deviation.

• To explore different types of distributions.

What is the assumed population standard deviation in the problem?

• $30.0

• $20.3

• $25.0

• $15.0

What confidence level is desired for the estimate?

• 90%

• 95%

• 85%

• 99%

What is the error margin for the estimate of average spending?

• $3.0

• $1.5

• $2.0

• $2.5

What is the area to the right of the z-score for a 95% confidence interval?

• 0.15

• 0.025

• 0.05

• 0.10

Which function is used in the graphing calculator to find the z-score?

• Normal CDF

• Mean Calculation

• Inverse CDF

• Standard Deviation

What is the rounded z-score used in the sample size calculation?

• 2.05

• 1.96

• 1.75

• 1.64

What is the formula used to calculate the sample size?

• n = (sigma / z) * e

• n = (z * e) / sigma

• n = (z + sigma) / e

• n = (z * sigma / e)^2

Why do we round up the sample size calculation?

• To ensure the sample size is not too small.

• To make calculations easier.

• To reduce the error margin.

• To match the z-score.

What is the final sample size needed according to the calculation?

• 260

• 250

• 253

• 254