Final answer:
When conducting a hypothesis test, the p-value is compared to the significance level to determine whether to reject or fail to reject the null hypothesis.
Step-by-step explanation:
When conducting a hypothesis test, the p-value is compared to the significance level (alpha) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than alpha, the null hypothesis is rejected, indicating that there is sufficient evidence to support the alternative hypothesis. On the other hand, if the p-value is greater than alpha, the null hypothesis is not rejected, indicating that there is not enough evidence to support the alternative hypothesis.
For example, in the first question, the p-value is given as 0.2150 and the significance level is 0.01. Since 0.2150 > 0.01, the null hypothesis is not rejected. Therefore, at a significance level of 0.01, there is not enough evidence to conclude that the science students spend more on textbooks than the humanities students.
To summarize, the decision to reject or fail to reject the null hypothesis is based on comparing the p-value to the significance level. If the p-value is less than the significance level, the null hypothesis is rejected and there is sufficient evidence to support the alternative hypothesis. If the p-value is greater than the significance level, the null hypothesis is not rejected and there is not enough evidence to support the alternative hypothesis.