Nationwide Insurance would like to perform a chi-square test to investigate whether a difference exists in the proportion of male and female teenagers who text while they drive. A random sample of 80 male teenagers found that 50 indicated they texted while driving. A random sample of 120 female teenagers found that 65 indicated they texted while driving. Using α = 0.5, the conclusion for this chi-square test would be that because the test statistic is

Since the test statistic is less than the critical value while using α = 0.5, the conclusion for this chi-square test would be that we cannot reject the null hypothesis and cannot conclude that there is a difference in the proportion of male and female teenagers who text while they drive.

Each statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is correct is called a chi-squared test.

Through sample variance or from a sum of squared, chi-squared test are often constructed from them. Rising from an assumption of independent normally distributed data are test statistics that follow a chi-squared distribution, which is valid in a lot of cases due to the central limit theorem.