Rare Events, the Sample, and the Decision and Conclusion · Exercise 13

Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.

Is σ known and, if so, what is it?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §9.4 Rare Events, the Sample, and the Decision and Conclusion · Exercise 13