An agricultural researcher wishes to see if kelp extract helps prevent frost damage on tomato plants. 100 tomato plants in individual containers are randomly assigned to 2 different groups. plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with kelp extract, while the plants in group 2 are not. after the first frost in the autumn, 12 of the 50 plants in group 1 exhibited damage. 18 of the 50 plants in group 2 showed damage. test the claim to see if there is evidence of a decrease in the proportion of tomatoes suffering frost damage for tomatoes sprayed with kelp extract.

a) state the hypotheses.

b) identify the p-value to the nearest thousandth.

c) state the conclusion in the context of the problem.

A null hypothesis is a statement, in which there is no relationship between two variables. An alternative hypothesis is statement in which there is some statistical significance between two measured phenomenon.

Group 1 n₁ = 50 , x₁ = 12

Group 2 n₂ = 50 , x₂ = 18

p₁ = x₁/n₁ = 12/50 = 0.24

p₂= x₂/n₂ = 18/50 = 0.36

Testing the null and alternative hypothesis

H₀ = p₁ - p₂= 0

Hₓ = p₁ - p₂ < 0

Level of Significance α =0.05

Test Statistic

[tex]\rm z = \dfrac{p_1-p_2}{\sqrt{\dfrac{p_1(1-p_1)}{n_2} +\dfrac{p_2(1-p_2)}{n_2}}}[/tex]

On substituting the values

z = -0.12/0.9086

z = -1.32

p value = p(z > -1.32)

p value = 0.0934

Therefore p value > 0.05

Hence we fail to reject H₀ at 5 % level of significance .

There is no significant evidence that the decrease in proportion of tomatoes suffering frost damage for tomatoes sprayed with the kelp extract.

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