Question

a genetic experiment involving peas yielded one sample of offspring consisting of 435 green peas and 175 yellow peas. use a 0.01 significance level to test the claim that under the same circumstances, 26% of offspring peas will be yellow. identify the null hypothesis, alternative hypothesis, test statistic, p - value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. use the p - value method and the normal distribution as an approximation to the binomial distribution.

what is the test statistic?
z = □
(round to two decimal places as needed.)

Explanation:

Step1: Calculate sample proportion

The sample size \(n = 435+175=610\). The number of yellow peas \(x = 175\). The sample proportion \(\hat{p}=\frac{x}{n}=\frac{175}{610}\approx0.287\).

Step2: Calculate test - statistic

The formula for the test - statistic \(z\) in a hypothesis test for a proportion is \(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\), where \(p = 0.26\) (the proportion in the null hypothesis), \(\hat{p}=0.287\), and \(n = 610\).

Substitute the values:

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Answer:

\(z = 1.52\)