In the snapdragon (Antirrhinum majus), individual plants can be red flowered, pink flowered, or white flowered

In the snapdragon (Antirrhinum majus), individual plants can be red flowered, pink flowered, or white flowered. According to a certain Mendelian genetic model, selfpollination of pink-flowered plants should produce progeny that are red, pink, and white in the ratio 1 : 2 : 1. A geneticist self-pollinated pink-flowered snapdragon plants and produced n = 234 progeny with the following colors: Type Red Pink White Number 54 122 58 Suppose we want to test the null hypothesis that the progeny actually follow the Mendelian ratio of 1 : 2 : 1 against a nondirectional alternative using a χ 2 goodnessof-fit test.

(a) What is the expected number of each color under the null hypothesis?

(b) Shown below is the output of the χ 2 test. Draw conclusion under a significance level of α = 0.10. Chi-squared test for given probabilities data: c(54, 122, 58) X-squared = 0.5641, df = 2, p-value = 0.7542