Final answer:
A higher value of the Chi-square statistic indicates a greater discrepancy between observed and expected frequencies, often leading to the rejection of the null hypothesis in favor of the alternative. This suggests, for instance, that science students may indeed spend more on textbooks than humanities students. The significance of the increase in the Chi-square value is also influenced by the degrees of freedom of the distribution.
Step-by-step explanation:
When conducting a Chi-square test, if the value of X2 (Chi-square statistic) increases, it suggests a greater discrepancy between the observed frequencies and the expected frequencies under the null hypothesis. A higher Chi-square value can lead to the rejection of the null hypothesis, indicating that there is a significant difference between the observed and expected data. This is particularly relevant if the calculated Chi-square value exceeds the critical value from the Chi-square distribution table at a given significance level (e.g., alpha level of 0.05).
In the context of hypothesis testing, rejecting the null hypothesis implies that there is sufficient evidence to support the alternative hypothesis (Ha), which, in the example provided, suggests that science students spend more on textbooks than humanities students. Moreover, as the Chi-square value increases, the corresponding p-value decreases; when the p-value falls below the chosen significance level, this constitutes statistical evidence against the null hypothesis.
It's also important to consider degrees of freedom when interpreting Chi-square results. As the degrees of freedom increase, the Chi-square distribution becomes more symmetrical, and its shape approaches that of a normal distribution. However, the mean and median of a Chi-square distribution are only the same when the degrees of freedom are high (e.g., df = 24).