Assignment: z-Test

Hypothesis testing is the foundation of conducting research in psychology. Researchers must first determine the question they wish to answer and then state their prediction in a null hypothesis and an alternative hypothesis. Once the hypotheses are stated, researchers move on to data collection. However, once the results come in, the real challenge is to determine if they have meaning; that is, are the results statistically significant or just due to random variation?
This application will allow you to practice hypothesis testing by using z-scores to compare a single score to a population mean in order to determine if results are statistically significant. Download the data set that you will use for this Assignment from the Weekly Data Set forum found in the Discussions area of the course navigation menu. Be sure to watch this week’s instructional video in the introduction or Learning Resources folder before beginning your Assignment.
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. You can find the data for this Assignment in the Weekly Data Set forum found on the course navigation menu.
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. You can find the information you need in the Weekly Data Set forum. Use it to calculate Monica’s raw math score by hand. Provide your calculations in your Assignment submission (i.e., explain your work).
Submit responses to the following:
Be sure to fully explain the rationale for your answer to each question, including evidence from the text and Learning Resources.
Provide an APA reference list.
Week 3 Data Set
Monica’s reading comprehension score = 107
Mean fourth grade reading comprehension score = 109
Standard deviation of the fourth grade’s reading comprehension = 0.6
Monica’s z-score in math = 2.4
Mean fourth grade math score = 210
Standard deviation of the fourth grade’s math scores = 11.1
Learning Resources
Heiman, G. (2015). Behavioral sciences STAT (2nd ed.). Stamford, CT: Cengage.
Chapter 5, “Describing Data with z-Scores and the Normal Curve” (pp. 68–84)
Chapter 6, “Using Probability to Make Decisions about Data” (pp. 88–102)
Chapter 7, “Overview of Statistical Hypothesis Testing: The z-Test” (pp. 106–123)
(I will upload them tomorrow morning)
and
Videos