please show working .. do not use computer or excel .thanks Q. 3. An agricultura

Question

please show working .. do not use computer or excel .thanks

Q. 3. An agricultural researcher wishes to know whether seed colour and petal colour in field beans are associated. She carried out a survey in which a random sample of 500 bean plants from the population of interest was taken and classified each plant according to seed colour and petal colour. The results obtained are summarised in the following table. Test the hypothesis at 5% level whether colours of seed and petal in the field beans are associated. (13 marks) Petal colour Seed colour Light brown 13 70 112 White Dark brown 21 Purple Mauve White Brown 32 102 59 14 10

Explanation / Answer

H0: There is no association between colours of seed and petal in the field beans
H1: There is association between colours of seed and petal in the field beans

Let the los be alpha = 5%

The observed frequencies are

The expected frequencies are

The chisquare contribution values are

Degrees of freedom: 6

Test Statistic, X^2: 58.5752
Critical X^2: 12.59157
P-Value: 0.0000

Here chisquare value > chisquare critical value and P-value < alpha 0.05 so we reject H0

Thus we conclude that  There is association between colours of seed and petal in the field beans

Seed Color Petal Color Dark Brown Brown Light Brown White Total Purple 21 32 13 4 70 Mauve 55 102 70 8 235 White 14 59 112 10 195 Total 90 193 195 22 500

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