1) Suppose we want to see if American children have higher levels of cholesterol than the average child (i.e., in the entire world - the total population). We find that the population average for cholesterol for children all over the world is 190. We test 25 US children and find an average of 201 with a standard deviation of 10. Conduct a hypothesis with a significance level of 0.05. What is the test statistic?
2) Police officers often have to call Child Protection Services (CPS) when responding to a call for service. However, when they encounter CPS workers, they are not always satisfied. The national average level of satisfaction police officers have with CPS workers is 6.5 (on a scale of 0-10, with 10 being most satisfied). The head of CPS in Phoenix wants to see if the satisfaction levels of the police with CPS are different in Phoenix. He talks to 200 Phoenix police officers and finds the average satisfaction level is 7.8, with a standard deviation of 2.7. Conduct a hypothesis test to determine if the Phoenix police officers' average level of satisfaction is truly different than the national average. Use a significance level of 0.01.
In the above hypothesis test, what is the test statistic?