Mendelian theory indicates that the shape and color of a certain vari- ety of pe

Question

Mendelian theory indicates that the shape and color of a certain vari- ety of pea ought to be grouped into four groups, "round and yellow," "round and green," "angular and yellow," and "angular and green," according to the ratios 9 : 3 : 3 : 1, For n 556 peas, the following were observed (the last column gives the expected number): Round and yellow 315 312.75 Round and green 108 104.25 Angular and yellow 101 104.25 Angular and green 32 34.75 Are the data consistent at the size of 0.05 with the null hypothesis Ho: P1 = 9/16. P2 = 3/16,P3 = 3/16 and p4 1/16?

Explanation / Answer

Her As per the given null hypothesis we will calculate the chi - square statistic

X2 = (315 - 312.75)2/312.75 + (108 - 104.25)2/104.25 + (101 - 104.25)2/104.25 + (32 - 34.75)2/34.75= 0.4700

so here Degree of freedom = 4 -1 = 3

and alpha = 0.05

so critical value X2critical = 7.8147

so here X2 < X2critical that means we failed to reject the null hypothesis and conclude that the data is consisitant here.

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