Review of Lessons 6.1-6.2

Front

What is the formula to calculate the sample size needed for estimating a population mean with a specified margin of error?

Back

n = (Z * σ / E)², where Z is the Z-score corresponding to the confidence level, σ is the population standard deviation, and E is the margin of error.

Front

Define 'confidence interval' in statistics.

Back

A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter, with a specified level of confidence.

Front

What is the significance of the Z-score in confidence intervals?

Back

The Z-score represents the number of standard deviations a data point is from the mean, and it is used to determine the width of the confidence interval based on the desired confidence level.

Front

How do you calculate the margin of error for a confidence interval?

Back

Margin of error (E) = Z * (σ / √n), where Z is the Z-score, σ is the population standard deviation, and n is the sample size.

Front

What is the standard deviation and why is it important in statistics?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It is important because it helps to understand the spread of data points around the mean.

Front

What does a 95% confidence level mean?

Back

A 95% confidence level means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population mean.

Front

How do you construct a confidence interval for a population mean when the population standard deviation is known?

Back

Use the formula: CI = (x̄ - E, x̄ + E), where x̄ is the sample mean and E is the margin of error.

Front

What is the relationship between sample size and margin of error?

Back

As the sample size increases, the margin of error decreases, leading to a more precise estimate of the population mean.

Front

What is the formula for calculating the confidence interval for a population mean when the sample size is small (n < 30)?

Back

Use the t-distribution: CI = (x̄ - t*(s/√n), x̄ + t*(s/√n)), where t is the t-score, s is the sample standard deviation, and n is the sample size.

Front

Define 'population mean' (μ).

Back

The population mean (μ) is the average of all possible values in a population.