13. Chi-Square Tests & Goodness of Fit

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?

Which of the following is not a requirement to conduct a $\chi ²$ goodness-of-fit test?

In a Chi Square Goodness of Fit Test, how do you calculate the expected value for each category?

Which of the following best describes the possible values for a chi-square statistic in a goodness of fit test?

Weather-Related Deaths For the most recent year as of this writing, the numbers of weather-related U.S. deaths for each month were 61, 14, 22, 26, 29, 42, 93, 49, 47, 35, 96, 16, listed in order beginning with January (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Provide an explanation for the result.

A gym owner wants to know if the gym has similar numbers of members across different age groups. The table shows the distribution of ages for members from a random survey. Write the null & alt. hypotheses to test the claim that the gym has equal numbers of members across all age groups.