Scenario: Lucy wants to know how her fourth-grade daughter, Monica, scored on a test of reading comprehension compared to the population of other fourth graders in the school district. Luckily, Lucy has taken this course and knows that a z-score will help her understand Monica's reading score in relation to the population.

1. State the dependent variable.
2. Explain whether Lucy should use a one-tailed or a two-tailed z-test and explain why.
3. State the null hypothesis in words (not formulas).
4. State the alternative hypothesis in words (not formulas).
5. Calculate the obtained z-score by hand. Describe your calculations (i.e., show your work).
6. When alpha is set at .05, the critical value is ± 1.96. Should the null hypothesis be retained or rejected? Explain why.
7. Are the results statistically significant? How do you know?
8. What should Lucy conclude about Monica's reading comprehension score in comparison to the population?
9. Lucy is excited that she remembers how to compute a z-score and does some additional computations to find Monica's z-score in math. Calculate Monica's raw math score by hand. (explain your work).

Monica's reading comprehension score = 27   Mean fourth grade reading comprehension score = 21   Standard deviation of the fourth grade's reading comprehension = 1.8   Monica's z-score in math = 1.2   Mean fourth grade math score = 79   Standard deviation of the fourth grade's math scores = 3.1