Question

The basis for rejecting any null hypothesis is arbitrary. The researcher can set more or less stringent standards by deciding to raise or lower the \(p\) value used to reject or not reject the hypothesis. 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.

Short answer

Answer: Using a p-value of 0.10 in a chi-square analysis of genetic crosses is less stringent about not rejecting the null hypothesis compared to lower p-values such as 0.05 or 0.01. It allows for a higher chance of accepting the null hypothesis even if there might be significant differences between the observed and expected ratios.

Step-by-step solution

Understanding p-value and null hypothesis

A p-value is a probability value that allows us to determine if there's enough evidence to reject the null hypothesis. The null hypothesis (\(H_0\)) states that there is no significant difference between the observed and expected values. The smaller the p-value, the more evidence we have that the observed and expected values are not equal, which means we can reject the null hypothesis. Typically, a p-value of \(0.05\) or lower is considered significant evidence to reject the null hypothesis.

Chi-square analysis in genetic crosses

In the context of genetic crosses, chi-square analysis is used to determine if the observed ratios in a genetic cross follow the expected ratios based on Mendelian inheritance. The null hypothesis, in this case, would be that the observed ratios follow the expected ratios. If the p-value is less than the chosen significance level (alpha), we reject the null hypothesis, indicating that the observed ratios do not follow the expected ratios and there might be some other factors influencing the genetic cross.

Stringency of p-value in chi-square analysis

Using a p-value of \(0.10\) is less stringent about not rejecting the null hypothesis than a lower p-value (such as 0.01 or 0.05). When the p-value is larger, it is harder to reject the null hypothesis, meaning there is a higher chance of accepting it even if there might be significant differences between the observed and expected values. More stringent standards imply using a smaller p-value, which increases the chances of rejecting the null hypothesis when there is a significant difference between the observed and expected values.

Conclusion

In the case of chi-square analysis of genetic crosses, using a p-value of \(0.10\) is less stringent about not rejecting the null hypothesis. This means that there will be a higher chance of accepting the null hypothesis (i.e., the ratios follow Mendelian inheritance) even if there might be significant differences between the observed and expected ratios.