PSYC 3002 – Week 3 Assignment – z-Test
Monica’s reading comprehension score = 107
Mean of the 4th-grade reading comprehension score = 109
Std. Deviation of the 4th grade’s reading comprehension =
0.6. Monica’s z-score in math = 2.4
Mean of the 4th grade math score = 210
Std. Deviation of the 4th grade’s math scores = 11.1
The dependent variable in this scenario is Monica’s test scores. A dependent variable is what is measured in an experiment and is influenced by the independent variable. (Heiman, 2015) In this scenario, Monica’s test scores are being measured, and they are dependent upon her reading comprehension and math tests.
In this scenario, Lucy should use a two-tailed test. The difference between a one-tailed test and a two-tailed test is that a two-tailed test does not predict how the scores will change, but a one-tailed test does. (Heiman, 2015) In this situation, Lucy wants to know how Monica’s score compares to others. She mentions nothing about expecting Monica’s scores to increase or decrease, so for this reason, she should use a two-tailed test.
The null hypothesis states that Monica’s test scores are less than, or equal to, the average scores of the population. The null hypothesis says that there is no relationship between the independent and dependent variables. (Heiman, 2015)
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PSYC 3002 – Week 3 Assignment – z-Test
The alternative hypothesis says that Monica’s test scores are higher than the average scores of the population. The alternative hypothesis is basically the opposite of the null hypothesis, stating that there is a relationship between the two variables. (Heiman, 2015)
To calculate the obtained z-score, we use the formula z = X−µ σ x, which is the formula for transforming a raw score into a z-score. We have to determine what numbers go where. X represents the raw score. Monica’s reading score is 107, so X = 107. µ represents the population mean. The mean of the 4th-grade reading scores is 109. So, µ = 109. σ x represents the standard deviation. The standard deviation of the 4th-grade reading comprehension is 0.6. So, σ x = 0.6.
Therefore, z = X−µ
|
=x 107−109
0.6 . Next, you solve the numerator, subtracting −2 109 from 107, which equals -2. So, z = -3.33.
When the alpha is set at .05, the critical value is ± 1.96, and the calculated z- score is -3.33, then the null hypothesis should be rejected. Basically, the alpha and critical values say that it is very likely the z-score will fall between -1.96 and +1.96. Since it does not, it should be rejected because the z-score is very unlikely.
Lucy should conclude that Monica’s reading comprehension score is above average when compared to the rest of the population’s scores.
The formula to transform a z-score into a raw score is X = (z)( Sx ) + X̄. (Heiman, 2015.) X represents the raw score, which is what we are looking for based on the other information obtained. Z refers to Monica’s z-score in math, which is 2.4. Sx represents the standard deviation, which is 11.1. X̄ represents the mean, which is 210. So, X = (z)( Sx ) + X̄ is now X = (2.4)(11.1) + 210. First, you multiply the mean and standard deviation, which is 2.4 times 11.1 and equals 26.64. Now, you have 26.64 + 210, which equals 236.64. So X = 236.64. This means that Monica scored 236.64 on her math test.
References
Heiman, G. (2015). Behavioral sciences STAT (2nd ed.). Stamford, CT: Cengage.
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Question 
PSYC 3002 – Week 3 Assignment – z-Test
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).4.
State the alternative hypothesis in words (not formulas).5.Calculate the obtained z-score by hand. Describe your calculations