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.
- State the dependent variable.
- Explain whether Lucy should use a one-tailed or a two-tailed z-test and explain why.
- State the null hypothesis in words (not formulas).
- State the alternative hypothesis in words (not formulas).
- Calculate the obtained z-score by hand. Describe your calculations (i.e., show your work).
- When alpha is set at .05, the critical value is ± 1.96. Should the null hypothesis be retained or rejected? Explain why.
- Are the results statistically significant? How do you know?
- What should Lucy conclude about Monica's reading comprehension score in comparison to the population?
- 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