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. The data is as follows:

Monica’s reading comprehension score = 22
Mean fourth grade reading comprehension score = 19
Standard deviation of the fourth grade’s reading comprehension = 1.8
Monica’s z-score in math = 2.2
Mean fourth grade math score = 180
Standard deviation of the fourth grade’s math scores = 11.8

Please help me find the following:
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
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?

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