Step 1 :The null hypothesis is \(H_{0}: p = 0.27\) and the alternative hypothesis is \(H_{1}: p \neq 0.27\).
Step 2 :The sample proportion \(\hat{p}\) is calculated as the number of yellow peas divided by the total number of peas, which is \(\frac{135}{565} = 0.239\).
Step 3 :The hypothesized population proportion \(p_{0}\) is given as 0.27.
Step 4 :The sample size \(n\) is the total number of peas, which is 565.
Step 5 :The test statistic in a hypothesis test for a proportion is a z-score, which is calculated using the formula \(z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}\).
Step 6 :Substituting the values into the formula, we get \(z = \frac{0.239 - 0.27}{\sqrt{\frac{0.27(1-0.27)}{565}}} = -1.66\).
Step 7 :Final Answer: The test statistic is \(\boxed{-1.66}\).