13. Chi-Square Tests & Goodness of Fit

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. Does this data set fit the criteria for a G.O.F. test?

For which of the following scenarios is a chi-square $\chi 2^{}$ goodness-of-fit test most appropriate?

Which of the following is not a requirement to conduct a $\chi -\mathrm{square}$ goodness-of-fit test?

Which of the following is not a condition for a chi-square goodness-of-fit test?

Roulette Wheel A pit boss suspects that a roulette wheel is out of balance. A roulette wheel has 18 black slots, 18 red slots, and 2 green slots. The pit boss spins the wheel 500 times and records the following frequencies:

Is the wheel out of balance? Use the α = 0.05 level of significance.

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

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

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?

Performing a Chi-Square Goodness-of-Fit Test

In Exercises 7–16, (a) identify the claim and state H₀ and Hₐ, (b) find the critical value and identify the rejection region, (c) find the chi-square test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Births by Day of the Week A doctor claims that the number of births by day of the week is uniformly distributed. To test this claim, you randomly select 700 births from a recent year and record the day of the week on which each takes place. The table shows the results. At α=0.10, test the doctor’s claim. (Adapted from National Center for Health Statistics)

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 Problems 7–10, determine (a) the chi-square test statistic.

H0: pA=pB=pC=pD=pE=1/5

H1: At least one of the proportions is different from the others.

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