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Chapter 12: Problem 6

Two pea plants are crossed, and a ratio of 3 yellow plants to 1 green plant is expected in the offspring. It is found that out of 100 plants phenotyped, 84 are yellow and 16 are green. Do the experimental data match the expected data? (A) Yes, the \(\chi^{2}\) value is greater than 3.84 . (B) Yes, the \(\chi^{2}\) value is smaller than \(3.84 .\) (C) No, the \(\chi^{2}\) value is greater than 3.84 . (D) No, the \(\chi^{2}\) value is smaller than 3.84 .

Short Answer

Expert verified
(C) No, the χ² value is greater than 3.84.

Step by step solution

01

Identify Observed and Expected Frequencies

The problem provides us with the observed frequencies: 84 yellow plants and 16 green plants. The expected ratio is 3 yellow plants to 1 green plant. If we have 100 plants, we expect 3/4 of them to be yellow and 1/4 of them to be green. Thus, the expected frequencies are 75 yellow plants and 25 green plants.
02

Calculate the χ² Value

To calculate the χ² value, we use the formula: \[\chi^2 = \sum \frac{(O-E)^2}{E}\] where \(O\) represents the observed frequency and \(E\) represents the expected frequency. For yellow plants: \[\frac{(84-75)^2}{75} = \frac{(9)^2}{75} = \frac{81}{75}\] For green plants: \[\frac{(16-25)^2}{25} = \frac{(-9)^2}{25} = \frac{81}{25}\] Summing the two values, we find: \[\chi^2 = \frac{81}{75} + \frac{81}{25} = 1.08 + 3.24 = 4.32\]
03

Compare χ² Value to the Critical Value

Now we need to compare the calculated χ² value (4.32) with the critical value (3.84). If the χ² value is greater than the critical value, the experimental data doesn't match the expected data. In this case, the χ² value (4.32) is greater than the critical value (3.84). Therefore, the correct answer is: (C) No, the χ² value is greater than 3.84.

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Most popular questions from this chapter

Given the cross \(A a B b C c \times A a B b C c\), what is the probability of having an \(A A B b C C\) offspring? (A) \(\frac{1}{4}\) (B) \(\frac{1}{8}\) (C) \(\frac{1}{16}\) (D) \(\frac{1}{32}\)

Five subjects were weighed before and after an 8-week exercise program. What is the average amount of weight lost in pounds for all five subjects, rounded to the nearest pound? $$\begin{array}{|c|c|c|} \hline \text { Subject } & \begin{array}{c} \text { Starting } \\ \text { Weight } \\ \text { (pounds) } \end{array} & \begin{array}{c} \text { Final } \\ \text { Weight } \\ \text { (pounds) } \end{array} \\ \hline 1 & 184 & 176 \\ \hline 2 & 200 & 190 \\ \hline 3 & 221 & 225 \\ \hline 4 & 235 & 208 \\ \hline 5 & 244 & 225 \\ \hline \end{array}$$ (A) 12 pounds (B) 13 pounds (C) 14 pounds (D) 15 pounds

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Given the cross \(A a B b \times a a b b\), what is the probability of having an \(A a b b\) or aaBb offspring? (A) \(\frac{1}{2}\) (B) \(\frac{1}{4}\) (C) \(\frac{1}{16}\) (D) 0
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