AP Stats Chapter 11

Front

What is the chi-square (χ²) distribution?

Back

The chi-square (χ²) distribution is a probability distribution that is used in statistical hypothesis testing, particularly in tests of independence and goodness of fit. It is defined only for positive values and is skewed to the right.

Front

What does the term 'degrees of freedom' mean in the context of the chi-square distribution?

Back

Degrees of freedom refer to the number of independent values or quantities that can vary in an analysis without violating any constraints. In the chi-square distribution, it is typically calculated as the number of categories minus one.

Front

How does the shape of the chi-square distribution change with increasing degrees of freedom?

Back

As the degrees of freedom increase, the chi-square distribution becomes more symmetric and approaches a normal distribution.

Front

What is the mean of a chi-square distribution?

Back

The mean of a chi-square distribution is equal to the degrees of freedom (df).

Front

What is the relationship between the mean and median of a chi-square distribution?

Back

For a chi-square distribution, the mean is greater than the median, especially for lower degrees of freedom.

Front

What is the variance of a chi-square distribution?

Back

The variance of a chi-square distribution is equal to twice the degrees of freedom (df).

Front

What is a common application of the chi-square test?

Back

The chi-square test is commonly used to determine if there is a significant association between categorical variables in a contingency table.

Front

What is the formula for the chi-square statistic?

Back

The chi-square statistic is calculated using the formula: χ² = Σ((O - E)² / E), where O is the observed frequency and E is the expected frequency.

Front

What does a high chi-square statistic indicate?

Back

A high chi-square statistic indicates a significant difference between observed and expected frequencies, suggesting that the null hypothesis may be rejected.

Front

What is the significance level (alpha) in hypothesis testing?

Back

The significance level (alpha) is the threshold for determining whether to reject the null hypothesis, commonly set at 0.05 or 0.01.