Understanding Confidence Intervals and Sample Size

Della aims to estimate the proportion of her community that supports a tax increase for school funding. She needs to determine the smallest sample size to achieve a margin of error of no more than 2% at a 95% confidence level. The video explains confidence intervals, the role of critical values, and how to use a Z-table. It also covers maximizing the margin of error by choosing a sample proportion of 0.5 and solving algebraically for the minimum sample size required.

What is Della trying to estimate in her community?

• The average income of community members

• The proportion of community members favoring a tax increase

• The total population of the community

• The average age of community members

What does the confidence interval represent in statistics?

• The range of possible sample sizes

• The range within which the true population parameter is expected to lie

• The average value of the sample data

• The total number of observations in a sample

What does the margin of error represent in a confidence interval?

• The range of error allowed in the estimate

• The range of possible sample sizes

• The average value of the sample data

• The total number of observations

What critical value corresponds to a 95% confidence level?

• 1.64

• 1.96

• 2.58

• 2.33

What is the purpose of using a z-table in this context?

• To find the mean of the sample

• To estimate the population size

• To determine the critical value for a given confidence level

• To calculate the standard deviation

What is the significance of the number 1.96 in the context of confidence intervals?

• It is the critical value for a 95% confidence level

• It is the standard deviation

• It is the sample size

• It is the mean of the sample

Why is the value 0.5 used for p-hat when calculating the sample size?

• It minimizes the margin of error

• It represents the average of the sample

• It is the default value for all calculations

• It maximizes the margin of error

Why is it important to maximize the expression p-hat times 1 minus p-hat?

• To minimize the sample size

• To find the average of the sample

• To reduce the standard deviation

• To ensure the largest possible margin of error is considered

What is the minimum sample size Della should take to ensure her margin of error is no more than 2%?

• 2,401

• 2,500

• 2,000

• 2,100

What happens if the calculated sample size is not a whole number?

• Ignore the decimal part

• Round down to the nearest whole number

• Round up to the nearest whole number

• Use the exact decimal value