Question

section 9.3 homework
score: 0/7 answered: 0/7
question 1
the $\chi^{2}$ distribution is
left-tailed
two-tailed
right-tailed

Explanation:

The $\chi^{2}$ distribution is a continuous probability distribution. The $\chi^{2}$ statistic is calculated as a sum of squared terms. Since the sum of squared values is non - negative ($\chi^{2}=\sum\frac{(O - E)^{2}}{E}\geq0$ where $O$ is the observed frequency and $E$ is the expected frequency), the values of the $\chi^{2}$ statistic range from $0$ to $\infty$. As a result, the $\chi^{2}$ distribution is skewed to the right. In hypothesis testing using the $\chi^{2}$ distribution (such as goodness - of - fit tests and tests of independence), we are typically interested in the upper (right) tail of the distribution because large values of the $\chi^{2}$ statistic indicate a poor fit between the observed and expected data (in goodness - of - fit tests) or a significant association (in tests of independence).

Answer:

right - tailed