Level 4: Inference · Problem 61 of 87

Chi-square goodness of fit

A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.

The task

A call center schedules staff on the assumption that calls are spread evenly across the five weekdays. Last period the observed counts were: Mon 33, Tue 27, Wed 23, Thu 25, Fri 17 (total 125). Compute the chi-square goodness-of-fit statistic, then decide at α = 0.05 whether the counts depart from the expected distribution. Round to 2 decimal places.

What this problem teaches

The formula: χ² = Σ (O - E)² / E, E = N × expected share, df = k - 1. Divide by the expected count, not the observed one, and keep expected counts at 5 or more for the approximation to hold. A large statistic means the observed mix does not fit the expected shares.

A hint if you get stuck

Expected count for each category = total × its expected share. χ² = Σ (O - E)² / E, with k - 1 degrees of freedom.