Question

Using a significance level of p=0.05, which of the following statements best completes a chi-square goodness-of-fit test for a model of independent assortment based on Table 5-3? A) The calculated chi-square value is 0.66, and the critical value is 0.05. The null hypothesis can be rejected. B) The calculated chi-square value is 0.66, and the critical value is 3.84. The null hypothesis cannot be rejected. C) The calculated chi-square value is 3.91, and the critical value is 5.99. The null hypothesis can be rejected. D) The calculated chi-square value is 3.91, and the critical value is 7.82. The null hypothesis cannot be rejected.

Answer 1

Option B is correct as the calculated chi-square value of 0.66 is less than the critical value of 3.84 at the p=0.05 level, meaning the null hypothesis cannot be rejected in this chi-square goodness-of-fit test.

Step-by-step explanation:

When conducting a chi-square goodness-of-fit test, we compare the calculated chi-square value with the critical value at a chosen significance level to decide whether to reject or not reject the null hypothesis. Looking at the options provided, one can see that each option presents a different scenario with its own calculated chi-square value and critical value.

In this case, we are working with a significance level of p=0.05. The correct critical value for a chi-square test is determined based on the degrees of freedom (df) and the significance level, and not the calculated chi-square statistic itself. The calculated chi-square value is compared to this critical value to make a decision.

From the options given, Option B states a calculated chi-square value of 0.66 and a critical value of 3.84. This setup implies that the calculated value is lower than the critical value; therefore, we do not have enough evidence to reject the null hypothesis at the 0.05 significance level.