Question

A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 70% of the offspring resulting from this cross will have red flowers. To test this, 80 seeds from this cross were collected and germinated and 46 plants had red petals.

(a) Is there sufficient evidence at the 0.02 significance level to indicate the proportion of the hybrid plants with red petals differs from 70%? Use the P-value method in your test

(b) What would a Type I error be in this case?

Answer 1

Answer a)

(2) Level of Significance

The significance level is α = 0.02

(4) Decision about the null hypothesis

P-value corresponding to z = -2.44 for a two tailed test is 0.0147

[Obtained using Excel function =2*NORM.S.DIST(-2.44,TRUE)]

Since p-value = 0.0147 < α = 0.02, we reject the null hypothesis.

(5) Conclusion

At 0.02 significance level, there is sufficient evidence to indicate that the proportion of the hybrid plants with red petals differs from 70%

Answer b)

Type I error is rejecting null hypothesis even when it is true.

In this case, type I error will be concluding that the proportion of the hybrid plants with red petals differs from 70%, even when the true proportion is 70%.