1. A botanist has produced a new variety of hybrid wheat that is better able to

Question

1. A botanist has produced a new variety of hybrid wheat that is better able to withstand drought than other varieties. The botanist knows that for the parent plants, the proportion of seeds germinating is 80%. The proportion of seeds germinating for the hybrid variety is unknown, but the botanist claims that it is 80%. To test this claim, 400 seeds from the hybrid plant are tested, and it is found that 312 germinate. Use a 5% level of significance to test the claim that the proportion of germinating seeds for the hybrid is 80%.

Explanation / Answer

a.) H0 : P = 0.80
b.) H1 : P 0.80
c.)The test is a two-tailed test.For 0.05 the critical values are z = 0 1.96 .
d.) The number of trials is n = 400, and the number of successes is r = 312
pˆ = r/n = 312/400 = 0.78
e)  H0 : P = 0.80
q = 1 – p = 0.20
z = pˆ - p/ sqrt(pq/n)
z = (0.78 - .80)/ sqrt(.80 x .20)/400) = -1

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