A national retail firm is determining whether they will purchase a smaller company. The larger firm wants to know what percent of the smaller company's annual sales occurs in each season of the year. The smaller company provides the following information:

A

Spring: $18\%$

Summer: $21\%$

Fall: $23\%$

Winter: $38\%$

The larger firm collects the financial records of the smaller company in advance of the sale. The annual sales of the firm totaled $$23,864,000$ and were dispersed across the seasons in the following manner:

Spring: $$5,488,720$

Summer: $$6,443,280$

Fall: $$4,534,160$

Winter: $$7,397,840$

The larger firm wants to determine whether the data depicted in the financial records fits with the information previously provided to them by the senior leadership of the smaller company.

Perform Chi$-$Square test

What are the null and alternative hypothesis for the test?

$$ With $95\%$ confidence, does the observed data fit the expected data?

$$ What considerations or concerns might the larger firm have in advance of the acquisition of the smaller company?