Confidence Intervals for Means

What is a confidence interval?

• A confidence interval is a measure of how confident an individual is in their own abilities.

• A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter.

• A confidence interval is a statistical measure of the reliability of the data.

• A confidence interval is a range of values that is likely to contain the true value of a sample statistic.

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CCSS.HSS.IC.B.4

When constructing a confidence interval for the mean, what is the formula used?

• x̄ ± z * (σ / √n)

• x̄ ± z * (σ / n)

• x̄ ± z * (σ / n^2)

• x̄ ± t * (σ / √n)

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CCSS.HSS.IC.B.4

If the confidence level is increased, what happens to the width of the confidence interval?

• Remains the same

• Fluctuates

• Increases

• Decreases

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CCSS.HSS.IC.B.4

What is the purpose of using a confidence interval for the mean?

• To estimate the precision and reliability of the sample mean as an estimate of the population mean.

• To identify outliers in the sample

• To calculate the range of the data

• To determine the mode of the data

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CCSS.HSS.IC.B.4

What is the significance level often used in constructing confidence intervals?

• 0.25

• 0.05

• 0.10

• 0.01

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CCSS.HSS.IC.B.4

Explain the concept of margin of error in the context of confidence intervals for means.

• Margin of error is only applicable to categorical data, not means.

• The margin of error is the range of values within which the true population mean is guaranteed to fall.

• The margin of error is the amount added to and subtracted from the sample mean to create the confidence interval.

• Margin of error is not affected by sample size or confidence level.

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CCSS.HSS.IC.B.4

How does sample size affect the width of a confidence interval?

• Increasing sample size decreases the confidence interval but increases the margin of error.

• Sample size has no impact on the width of a confidence interval.

• Sample size and width of a confidence interval are directly related.

• Sample size and width of a confidence interval are inversely related.

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CCSS.HSS.IC.B.4

What is the relationship between standard deviation and the width of a confidence interval?

• Standard deviation and the width of a confidence interval are inversely proportional.

• Standard deviation and the width of a confidence interval are unrelated.

• Standard deviation and the width of a confidence interval are directly proportional.

• Standard deviation has no impact on the width of a confidence interval.

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CCSS.HSS.IC.B.4

What is the critical value and how is it used in constructing confidence intervals?

• The critical value is used in constructing confidence intervals by determining the margin of error around the sample estimate.

• The critical value is used to calculate the mean of the sample data

• The critical value is a measure of the variability within the sample data

• The critical value is used to determine the sample size needed for a confidence interval

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CCSS.HSS.IC.B.4

Discuss the importance of interpreting a confidence interval correctly.

• It helps in understanding the precision and reliability of the estimate derived from the sample data.

• It only applies to small sample sizes

• It is irrelevant in statistical analysis

• It helps in increasing the margin of error in the estimate

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CCSS.HSS.IC.B.4