Front

What is a confidence interval?

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. It is associated with a confidence level that quantifies the level of confidence that the parameter lies within the interval.

Front

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

Back

The margin of error represents the maximum expected difference between the true population parameter and a sample estimate. It indicates the range within which the true value is expected to lie.

Front

How does sample size affect the margin of error in a confidence interval?

Back

As the sample size increases, the margin of error decreases, leading to a more precise confidence interval. A larger sample provides more information about the population.

Front

What is the formula for calculating the sample size needed for a specific margin of error?

Back

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

Front

What is the Z-value for a 95% confidence level?

Back

The Z-value for a 95% confidence level is approximately 1.96.

Front

True or False: A wider confidence interval indicates a higher level of uncertainty about the population parameter.

Back

True.

Front

If a 95% confidence interval for a population mean is (50, 70), what can we infer about the population mean?

Back

We can infer that we are 95% confident that the true population mean lies between 50 and 70.

Front

True or False: Increasing the confidence level will result in a narrower confidence interval.

Back

False.

Front

What is the relationship between confidence level and margin of error?

Back

As the confidence level increases, the margin of error also increases, resulting in a wider confidence interval.

Front

What does it mean if a confidence interval does not contain the value of a population mean?

Back

It suggests that the sample data provides evidence that the population mean is likely not equal to that value.