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

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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