Answer to Question #229022 in Statistics and Probability for nat

Question

2.2 A farming cooperative in the KwaMashu buys wheat seeds for its farmer members from seed merchants. A particular seed merchant claims that their wheat seeds have at least an 80% germination rate. Before the farming cooperative will buy from this seed merchant, they want to verify this claim. A random sample of 320 wheat seeds supplied by this seed merchant was tested, and it was found that only 230 seeds germinated. Is there sufficient statistical evidence at the 3% significance level to justify the purchase of wheat seeds from this seed merchant? Use the p-value approach to conduct a hypothesis test for a single proportion, and report the findings to the KwaMashu farming cooperative. 

Answer 1

Sample proportion: $\hat p=\frac{230}{320}=0.7188.$

$H_0:\pi=0.8.$

$H_a:\pi<0.8.$

Test statistic: $z=\frac{0.7188-0.8}{\sqrt{\frac{0.8(1-0.8)}{320}}}=-3.63.$

P-value: $p=P(Z<3.63)=0.0001.$

Since the p-value is less than 0.03, reject the null hypothesis.

There is no sufficient statistical evidence at the 3% significance level to justify the purchase of wheat seeds from this seed merchant.