Question

A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 80% of the offspring resulting from this cross will have red petals. But based on your experience, less than 80% of the offspring will have red petals. So, to verify whether the geneticist claim is true or not, you want to test the null hypothesis Ho: u = 0.80 by computing the test statistics. You collected and germinated 120 seeds from this cross, and found that only 75 plants had red petals. What is the value of the test statistics? Write your answer with 2 decimal places.

Answer 1

Solution:
Given in the question
Null hypothesis H0: mean = 0.8
Alternate Hypothesis H1: mean<0.8
sample proportion = 75/120 = 0.625
Z test statistic = (0.625-0.8)/sqrt(0.8*0.2/120) = -0.175/0.0365 = -4.79

If we assume alpha = 0.05 than Zcritical = -1.96
if Ztast stat is less than Critical value than we will reject the null hypothesis.
Here (-4.79<-1.96) so we will reject the null hypothesis. so we have significant evidence that less than 80% of the offspring will have red petals.