A local convenience store was curious that their customers' favorite vegetable is. Last year they asked all their customers and found that $34\%$ liked broccoli the most, $21\%$ peas, $18\%$ carrots, $17\%$ cabbage, and $10\%$ liked beans the most.
Recently a random sample of $123$ vegetable-buying customers found that $39$ liked broccoli the most, $23$ peas, $20$ carrots, $17$ cabbage, and $24$ liked beans the most.
A chi-squared goodness of fit test is performed and results show strong evidence ($p < 0.01$) that vegetable preference has recently changed over the year.
What is a major shortcoming to the conclusion that vegetable preference has recently changed over the year?