Rare Events, the Sample, Decision and Conclusion · Exercise 11

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was three years with a standard deviation of 1.8 years. 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 jail time has increased. Assume the distribution of the jail times is approximately normal.

What symbol represents the random variable for this test?

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

OpenStax, Introductory Statistics 2e · §9.4 Rare Events, the Sample, Decision and Conclusion · Exercise 11