Final answer:
The research question about whether the mean time students spend on homework has changed from the historical 2.5 hours leads to a null hypothesis that there is no change, formulated as H0: μ = 2.5 hours. A hypothesis test, like a t-test, is then conducted to see if any difference between the sample mean and the historical mean is significant.
Step-by-step explanation:
An example of a research question in which you need to test if the mean value of a variable is equal to its historical value could be: "Has the mean length of time students spend doing homework each week changed from the historical 2.5 hours?" The null hypothesis for this research question would be that there is no change in the mean length of time students spend doing homework per week from the historical value. In other words, the null hypothesis (H0) is: H0: μ = 2.5 hours. The alternate hypothesis (Ha) could be: Ha: μ ≠ 2.5 hours, meaning the mean time has changed.
To conduct a hypothesis test, you would collect a sample from the current student population, calculate the sample mean, and then perform a statistical test, such as a t-test, to determine if any observed difference between the sample mean and the historical mean is statistically significant.