A market gardener grows four different varieties of tomato: cherry, black, plum,

Question

A market gardener grows four different varieties of tomato: cherry, black, plum, and brandywine. A test is conducted whereby 40 seeds of each variety are sown under similar conditions, with the number of germinated and non-germinated seeds recorded. Hie results are as follows: a) Conduct a test, at LOC = 95%, for whether the seed germination rate for the market gardener's tomatoes are independent of, or dependent upon, the particular variety. Use the critical-value method. b) Using die p-value method, determine if your conclusion from Part (a) would be different for any common values of LOC.

Explanation / Answer

(a) LOC = 95%

H0 : seed germination rate for the market gardener's tomatoes are indepenedent of particular variety.

Ha ; seed germination rate for the market gardener's tomatoes are depenedent of particular variety.

We will do chi- square test here.

Here Observed table is given. We will calculate the expected table.

i.e. For Germinated CHerry Expeccted value = 99 * 40/160 = 24.75

& for Non- Germinted Brandywine Cherry Expected value = 40 * 61/ 160 = 15.25

So similarly the expected table

Value of X2 = (19 - 24.75)2 /24.75 + (33 - 24.75)2 /24.75 + (27 - 24.75)2 /24.75 + (20 - 24.75)2 /24.75 + (21- 15.25)2 /15.25 + (7- 15.25)2 /15.25 + (13- 15.25)2 /15.25 +  (20- 15.25)2 /15.25

= 13.645

Here dF = (4-1) * (2-1) =3 and alpha = 0.05

so X2 critical = 7.815

so here X2 > X2critical so we can reject the null hypothesis and can conclude that seed germination rate for the market gardener's tomatoes are depenedent of particular variety.

(b) Here we can calculate p - value (X2 > 13.645 ; dF = 3) = 0.0034

so Normal common LOC values 0.10, 0.05, 0.01, 0.005 are greater than the p - value so we can conclude that seed germination rate for the market gardener's tomatoes are depenedent of particular variety.

Tomato Variety Germinated Non - Germinated Total Cherry 24.75 15.25 40 Black 24.75 15.25 40 Plum 24.75 15.25 40 Brandywine 24.75 15.25 40 Total 99 61 160

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