Statistics Assignment
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.
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 below:
Data Set:
Monica’s reading comprehension score = 61
Mean fourth grade reading comprehension score = 54
Standard deviation of the fourth grade’s reading comprehension = 2.4
Monica’s z-score in math = 1.10
Mean fourth grade math score = 151
Standard deviation of the fourth grade’s math scores = 12.2
To complete this Assignment, submit responses to the following:
- State the dependent variable. A dependent variable measures the behavior or attitude of a participant and depends on the participant’s reaction to a condition, or the category of the independent variable that creates the situation under which participants are studied (Heiman, 2015). In this scenario, the dependent variable is Monica’s test scores because they depend on her reaction to the independent variable, which in this case are her reading and math tests. PLEASE CHECK MY ANSWER
2. Explain whether Lucy should use a one-tailed or a two-tailed z-test and explain why. A one-tailed test is preformed when you want to predict that the dependent scores, in this case Monica’s test score, will only increase or will only decrease (Heiman, 2015). A two-tailed test is used when you do not predict whether dependent scores will increase or decrease Heiman, 2015). Since it is not indicated in this week’s instructions that Lucy did or want to make any predictions about Monica’s tests score and a , I suggest that she use a two-tailed test z-test. PLEASE CHECK MY ANSWER
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).To obtain Monica’s z-score for reading, I had to subtract her raw reading comprehension score of 61 by the mean of all fourth grade reading comprehension scores , which is 54. Then I divided the difference of 7 by the standard deviation of the fourth grade’s reading comprehension, 7 divided by 2.4 is 2.92, which brings me to the conclusion that the z-score for Monica’s reading comprehension is positive 2.92 and it fall above the mean by 2.92 standard deviations (Heiman, 2015).
Z= (61-54)/2.4
Z= 2.92
PLEASE CHECK MY ANSWER
6. When alpha is set at .05, the critical value is ± 1.96. Should the null hypothesis be retained or rejected? Explain why. When alpha is set at .05 and the critical value is negative or positive 1.96, the null hypothesis should be rejected because…….THIS IS NOT ANSWER, I TRIED TO UNDERSTAND THIS BUT I AM LOST
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?
PLEASE FULLY EXPLAIN ALL CALCULATIONS AND ANSWERS TO QUESTIONS
