Final answer:
To obtain a p-value of 0.5 in an experiment with two degrees of freedom, the needed chi-square value would roughly equal the degrees of freedom, which is 2.
Step-by-step explanation:
The question asks what chi-square value is needed to have a p-value of 0.5 for an experiment with two degrees of freedom. To find this value, we use the chi-square distribution table. For two degrees of freedom, the chi-square value corresponding to a p-value of 0.5 is not typically listed in standard tables, as p-values are commonly associated with the 'tail' probabilities or the extremes of the distribution. However, a p-value of 0.5 suggests we are looking at the median of the distribution. Since the mean and median of a chi-square distribution are approximately the same when the degrees of freedom are large, and given the symmetry of the distribution, for two degrees of freedom, the chi-square value at the median would be roughly equal to the degrees of freedom, which is 2.