1. Does listening to music reduce stress? A sample of 225 university students took part in a study in which they listened to relaxing music once a day. After a month, they took a standardized anxiety measure and the sample's average score was 98. The population of all scores on the anxiety measure has a mean of 100 and a standard deviation of 7.5. Is the sample of students significantly different than the population? Use an alpha level of 0.05, and all four steps of hypothesis testing. b) Now calculate the effect size for the sample.
2. A researcher wants to know if exercise really does improve mood. She recruits 100 students to engage in 30 minutes of physical activity daily. At the end of the semester, the students take a mood inventory and the sample has an average score of 51. The mood inventory has a population mean of 50 with a standard deviation of 10. Does the group who exercised have a significantly higher score than the rest of the population? Use an alpha level of 0.05, and all four steps of hypothesis testing.