Question

the goodness of fit is measured by $x^{2}$. this statistic measures the amounts by which the observed values differ from their respective predictions to indicate how closely the two sets of values match.
the formula for calculating this value is
$x^{2}=\sum_{e}\frac{(o - e)^{2}}{e}$
where $o =$ observed and $e =$ expected.
the expected and observed data have been entered into the table below. carry out the operations indicated in the top row. in the last column, enter your answers to two decimal places. then add up the entries in the last column to find the $x^{2}$ value.
$x^{2}=sum\leftarrow$

Explanation:

Step1: Calculate deviation (\(o - e\))

For Green stem/long petals (\(aabb\)): \(239 - 225=14\)
For Purple stem/long petals (\(A - bb\)): \(231 - 225 = 6\)
For Green stem/short petals (\(aaB-\)): \(210 - 225=- 15\)
For Purple stem/short petals (\(A - B-\)): \(220 - 225=-5\)

Step2: Calculate \((o - e)^2\)

For Green stem/long petals (\(aabb\)): \(14^2 = 196\)
For Purple stem/long petals (\(A - bb\)): \(6^2=36\)
For Green stem/short petals (\(aaB-\)): \((-15)^2 = 225\)
For Purple stem/short petals (\(A - B-\)): \((-5)^2=25\)

Step3: Calculate \(\frac{(o - e)^2}{e}\)

For Green stem/long petals (\(aabb\)): \(\frac{196}{225}\approx0.87\)
For Purple stem/long petals (\(A - bb\)): \(\frac{36}{225}=0.16\)
For Green stem/short petals (\(aaB-\)): \(\frac{225}{225}=1\)
For Purple stem/short petals (\(A - B-\)): \(\frac{25}{225}\approx0.11\)

Step4: Calculate \(\chi^{2}=\sum\frac{(o - e)^2}{e}\)

\(\chi^{2}=0.87 + 0.16+1 + 0.11=2.14\)

Answer:

\(2.14\)