A researcher planted various kinds of seeds and recorded whether or not they germinated within 5 weeks. The following table gives the data.

(a) Consider the null hypothesis that type of seed is independent germination. The value of the expected cell count for the "Okra/Yes "cell is 32 × 20/57 = 11.23. Why is this correct? That is, explain the statistical reasoning that leads to (row total) × (column total) / (grand total) being the formula for an expected cell count.
(b) The value of the test statistic is 1.84. Conduct a test of the null hypothesis that type of seed is independent germination. Use α = 0.05. Provide all steps, including degrees of freedom, P-value, and conclusion.

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Type of seced Germinate? Okra Sunflower Eggplant Total Yes 12 32 25 57 Total 20 18 19