AP Stats - Unit 5 - Confidence Intervals: Means

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 used to estimate the uncertainty around a sample statistic.

Front

What does it mean if a confidence interval does not overlap between two sample means?

Back

If the confidence intervals of two sample means do not overlap, it suggests that the means are significantly different from each other.

Front

What is the formula for calculating the margin of error in a confidence interval?

Back

Margin of Error = z*(σ/√n), where z is the z-score corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

Front

What is the significance of the normality condition in hypothesis testing?

Back

The normality condition states that the sampling distribution of the sample mean should be approximately normally distributed, especially when the sample size is small (n < 30).

Front

What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Front

What is the difference between a one-sample t-test and a z-test?

Back

A one-sample t-test is used when the sample size is small (n < 30) and the population standard deviation is unknown, while a z-test is used when the sample size is large or the population standard deviation is known.

Front

What is the purpose of a hypothesis test?

Back

The purpose of a hypothesis test is to determine whether there is enough statistical evidence in a sample of data to infer that a certain condition holds for the entire population.

Front

What does it mean if a sample is not independent?

Back

A sample is not independent if the selection of one individual affects the selection of another, which can lead to biased results.

Front

What is the role of sample size in confidence intervals?

Back

Larger sample sizes generally lead to narrower confidence intervals, indicating more precise estimates of the population parameter.

Front

What is a Type I error in hypothesis testing?

Back

A Type I error occurs when the null hypothesis is rejected when it is actually true.