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In Flower Beetles, Pygmy (Py) Is Recessive to Normal Size

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In flower beetles, pygmy (py) is recessive to normal size (py+) , and red color (r) is recessive to brown (r+) . A beetle heterozygous for these characteristics was test-crossed to a beetle homozygous for pygmy and red. The following are progeny phenotypes from this testcross. py+r+180py+r22pyr+19pyr191 Total 412\begin{array} { l l r } p y ^ { + } & r ^ { + } & 180 \\p y ^ { + } & r & 22 \\p y & r ^ { + } & 19 \\p y & r & 191 \\\text { Total } && 412\end{array} Carry out a series of chi-square tests to determine if the two loci are assorting independently.
-What is the correct chi-square value and how many degree(s) of freedom should be used in its interpretation?


Definitions:

Particular Interval

A specific range within a set of data or a mathematical function, generally defined by its upper and lower bounds.

Grouped Frequency Distribution

A grouped frequency distribution organizes data into intervals or groups, showing the number of occurrences for each interval.

Number of Downloads

The total count of times a digital file, application, or piece of software has been downloaded by users.

Type of Music

A category or genre that classifies music according to shared traditions, characteristics, or conventions.

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