and 30 are found to be infested with whitefly

Question

Suppose that 10% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected, and 30 are found to be infested with whitefly

Assuming that the experiment satisfies the conditions of the binomial experiment, do the data indicate that the proportion of infested fields is greater than expected? Use the p-value approach, and test using a 5% significance level.

find the p value

Answer 1

Null and alternate hypotheses

H₀: p≤0.10

H_a: p>0.10

Calculate test statistic

Z = (p̂-p)/√[p̂(1-p̂)/n]

Z = (30/100-0.10)/√[30/100(1-30/100)/100]

Z ≈ 4.364

Our critical value for 95% confidence is Z=1.96. Because 4.364>1.96 (test statistic > critical value), we reject the null hypothesis. This means that we are 95% confident that the true population proportion is greater than 0.10, or 10%.

Hope this helped!