Question

In the case of the chi-square analysis of genetic crosses, would the use of a standard of p = 0.10 be more or less stringent about not rejecting the null hypothesis? Explain.

Answer 1

Answer:

Step-by-step explanation:

Hello!

The Chi-Square Goodness of Fit analysis is used when you need to compare if a categorical variable follows certain theoretical model (such as the mendelian genetical ratios)

Remember this type of Chi-Square test compares the differences between observed values in a sample with the expected values obtained from the theoretical model. If these differences are too big the result will be a big statistic value. This big number will indicate that the population doesn't follow the theoretical model and this rejecting the null hypothesis.

On the other hand, if what's observed and what's expected are similar, their differences will be small, leading to nor reject the null hypothesis.

Following this reasoning, you get that the Chi-Square Goodness of Fit test has ALWAY a one-tailed rejection region to the right.

Let's say that you have the genetic model 9:3:3:1, which means your study variable has four categories.

The Goodness to Fit test has k-1 degrees of freedom, where k represents the number of categories. If you compare the rejection regions of different levels of significance:

α: 0.10

$X^2_{k-1;\alpha-1} = X^2_{3;0.90}= 6.251$

α: 0.05

$X^2_{k-1;\alpha-1} = X^2_{3;0.95}= 7.815$

α: 0.01

$X^2_{k-1;\alpha-1} = X^2_{3;0.99}= 11.345$

As you can see the higher that significance level, the larger the rejection region is, which means that you are more likely to reject the null hypothesis. Using a 10% for the analysis means that it is more stringent about not rejecting the null hypothesis.

I hope this helps!