Based on reading Howell, D. C. (2016). Fundamental Statistics for the Behavioral Sciences (9th ed.). Belmont, CA: Wadsworth Publishing. ISBN: 978-1-305-65297-2 Chapter 8 , answer the following to the best of your ability. Feel free to use examples to help you explain your responses.

1. Similar to the examples provided earlier (SAT scores and stress level) and in Howell, develop an example describing the difference between distributions of individual scores and sampling distributions. How do sample means (M) and population means () differ?
2. Conceptually, what are the differences among a sample standard deviation (S), a population standard deviation (_x), and a population standard error of the mean (_m)?
3. As researchers, we are typically interested in finding out information about our research hypothesis,but we are forced to test and make statistical decisions about the null hypothesis. Why is it that we can't just test the research hypothesis?
4. Explain what it means to "reject the null hypothesis."
5. What are type I and type II errors? How do they relate to the null hypothesis and significance testing? How do they relate to each other?