PSYCH/625: Statistics For The Behavior SciencesRespond to the following DISSCUSSION QUESTION BELOW in a minimum of 175 words:You find out that the average 10th grade math score, for Section 6 of the local high school, is 87 for the 25 students in the class. The average test score for all 10th grade math students across the state is 85 for 1,800 students. The standard deviation for the state is 3.8.Answer the following questions:· What z score do you calculate?· What is the area between the mean and the z score found in Appendix A of the textbook?· What does this mean about the probability of this test score difference occurring by chance? Is it less than 0.05?RESPOND TO THE TWO CLASSMATES BE LOW, INSEPRATE RESPONSEWITH A WORD COUNT OF 125 EACH. WITH REFERENCES TO YOUR RESPONSES.Fregela CaffieHello Professor Lowe & class,A Z-score is a numerical measurement used in statistics of a value’s relationship to the mean (average) of a group of values, measured in terms of standard deviation from the mean (“Investopedia”, 2019). Z Scores are helpful when calculating the probability of a population. I’ve seen two different formulas with two different answers. I’m lost at which one is correct. I see the post the professor posted stating the formula isZ=(87-85)/(3.8/5)=2.63I understand how to set it up but why did we use the 0.05 in the formula to find the z score. I was thinking that we were only to tell if the probability of the test score difference occurring.Investopedia(2019). Retrieved from https://www.investopedia.com/terms/z/zscore.asp……………………………………………………………………………………..Shan SotoHello,Z- score- A parametric inferential statistical test of the null hypothesis for a single sample where the population variance is known. Jackson, S. L. (2017). The z-score is helpful when calculating the probability of a specific score. It also enables the comparison of two scores that are from different normal distributions.The p-value represents the probability of the something happening in a given event. It is of significance in a statistical hypothesis test. P-value is used to help reject the null hypothesis and provide a tiny level of significance. According to the text, the p value, or alpha level, indicates the probability of a Type I error. Jackson, S. L. (2017). If the probability is small, then the results were due to chance. That being said, it is more likely that the difference between the population and the sample mean is an important difference.ReferencesJackson, S. L. (2017) Statistics Plain and Simple. https://phoenix.vitalsource.com/#/books/9781337681728/recent

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