13. Chi-Square Tests & Goodness of Fit

Which of the following is not a goodness-of-fit measure used in the context of the $\chi ²$ goodness-of-fit test?

Which of the following best describes the purpose of the $\chi 2^{}$ Goodness of Fit Test in statistics?

When conducting a chi-square goodness-of-fit test, how are the expected counts for each category calculated?

Which of the following accurately describes the chi-square test for goodness of fit?

Which of the following is not a characteristic of the $\chi ^2$ distribution?

In a chi-square goodness of fit test, what does the null hypothesis ($H\_0$) specify about the population proportions or frequencies?

Which of the following lists the requirements that must be met to perform a $\chi ²$ goodness-of-fit test?

In a chi-square goodness of fit test for absences across days of the week, if the observed number of absences on Monday is $O$ and the expected number is $E$, what is the contribution of the Monday absences to the calculation of the chi-square test statistic?

A scientist conducts a chi-square goodness of fit test with $4$ categories and obtains observed frequencies of $18$, $22$, $20$, and $20$. The expected frequency for each category is $20$. Which of the following values is closest to the chi-square value the scientist calculated?

Which of the following is not a characteristic of the $\chi ^2$ distribution?

Which of the following is not a characteristic of the $\chi ^2$ distribution?

Which of the following is an appropriate description of the $\chi -\mathrm{square}$ distribution?

Which of the following best describes the purpose of the $\chi ²$ goodness of fit test in statistics?

Performing a Chi-Square Goodness-of-Fit Test

In Exercises 7–16, (b) find the critical value and identify the rejection region.

Ways to Pay A financial analyst claims that the distribution of people’s preferences on how to pay for goods is different from the distribution shown in the figure. You randomly select 600 people and record their preferences on how to pay for goods. The table shows the results. At α=0.01, test the financial analyst’s claim. (Adapted from Travis Credit Union)

Which of the following best describes the null hypothesis of a $\chi 2^{ }$ goodness of fit test?