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Trusting GOF Results

APSTAT-AEPF1T

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?

A

The sample size was too small.

B

The sample contains bias.

C

The expected counts do not meet conditions for a chi-squared goodness of fit test.

D

The p-value does not provide sufficient evidence of change at most alpha levels.

E

Not all vegetable preferences have greatly changed.