The HR manager at Hernandez Inc.reports that 40% of the company's job applicants have a bachelor's degree, 34% have an associate's degree and the remaining 26% have a high school diploma.You take a simple random sample of 200 applicants and find that 96 have a bachelor's degree, 70 have an associate's degree, and 34 have a high school diploma.You conduct a chi-square hypothesis test to establish whether this sample result is sufficient to reject a null hypothesis that the composition of Hernandez' job applicant population matches the HR manager's claim. Report the chi-square test statistic.
A)6.88
B)15.71
C)4.23
D)9.49

Question

Quizplus · Accepted Answer

The chi-square test statistic is calculated using the formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. For a sample of 200 applicants, the expected frequencies based on the HR manager's report are 80 for bachelor's degree (40% of 200), 68 for associate's degree (34% of 200), and 52 for high school diploma (26% of 200). The observed frequencies are 96, 70, and 34, respectively. Plugging these into the formula gives: $\chi^2 = \frac{(96-80)^2}{80} + \frac{(70-68)^2}{68} + \frac{(34-52)^2}{52} = \frac{256}{80} + \frac{4}{68} + \frac{324}{52} = 3.2 + 0.059 + 6.23 = 9.489$, which rounds to 9.49.

The HR Manager at Hernandez Inc