Question

In assessing data that fell into two phenotypic classes, a geneticist observed values of 250:150. She decided to perform a $χ$ ² analysis by using the following two different null hypotheses:
(a) the data fit a 3:1 ratio, and
(b) the data fit a 1:1 ratio.
Calculate the $χ$ ² values for each hypothesis. What can be concluded about each hypothesis?

Accepted Answer

Step 1: Identify the observed values and total number of observations. Here, the observed counts are 250 and 150, so the total is 250 + 150 = 400. Step 2: For hypothesis (a), where the expected ratio is 3:1, calculate the expected counts by dividing the total according to this ratio. The expected count for the first class is $$\frac{3}{4} 	imes 400$$, and for the second class is $$\frac{1}{4} 	imes 400. $$Step 3: For hypothesis (b), where the expected ratio is 1:1, calculate the expected counts by dividing the total equally. Each class is expected to have $$\frac{1}{2} 	imes 400$$ individuals. Step 4: Use the chi-square formula to calculate the chi-square value for each hypothesis:

$$\$$chi^{2}$$ = \sum \frac{(O - E)^2$}{E}$$

where $$O is $$the observed count and $$E is $$the expected count for each phenotypic class. Calculate this sum separately for each hypothesis using their respective expected counts. Step 5: Compare the calculated chi-square values to the critical chi-square value from the chi-square distribution table at the appropriate degrees of freedom (df = number of classes - 1) and significance level (commonly 0.05). If the calculated value is less than the critical value, the hypothesis fits the data well; if greater, the hypothesis is rejected.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Chi-Square (χ²) Test

Null Hypothesis in Genetic Ratios

Interpreting Chi-Square Results