A buyer for a t-shirt shop wants to compare the proportion of t-shirts of each size that are sold to the proportion that were ordered. The buyer counts the number of t-shirts of each size that are sold in a week.
The buyer performs a chi-square goodness-of-fit test to determine whether the proportions of t-shirt sizes sold are consistent with the proportion of t-shirt sizes ordered.
The largest difference between observed and expected sales is in the medium category. Consequently, this category has the largest contribution to the chi-square statistic, 0.355.
The overall chi-square statistic is 0.648 and has a p-value of 0.885. Because the p-value is greater than the significance level of 0.05, the buyer fails to reject the null hypothesis. The buyer concludes that there is not a significant difference between the observed t-shirt sales and the expected t-shirt sales.