DEALING WITH NORMAL DATA AND ZSCORES - Statistics Project Example

Section 2: DEALING WITH NORMAL DATA AND Z–SCORES Your Your College Section 2: Dealing with Normal Data and Z–ScoresThis study wants to know whether there is an effect of watching television throughout the week on students’ performance. For this analysis, data for students’ previous test score and current test score is collected. This paper will calculate students’ z-scores for their previous test and current test and will compare to see if there is any change in the z-score. In addition, this paper will also calculate what proportion of students’ z-scores are below 0.50.z-ScoresThe average previous test score of the students was 85.

22 and vary from the mean by about 7.28. The average current test score of the students is 82.06 and varies from the mean by about 9.05. The z-score of the students’ test grades can be calculated using below formula:Table 1 shows the student’s z-scores for their previous and current test grades. The maximum and minimum z-scores for the previous test score are 1.48 and -1.54, respectively. The maximum and minimum z-scores for the current test score are 1.76 and -1.55, respectively. Thus, there is no outlier in both the current and previous test scores as all the z-score values are in between -3 and +3.

A total of 9 students’ z-score decreased from the previous test to current test and a total of 9 students’ z-score increased from the previous test to current test. The theoretical normal distribution probability of a z-score below 0.50 is about 0.6915. The number of students whose z-score is below 0.50 in current score is 11. Thus, proportion of the students test scores on the current test only fall below z = .50 is about 0.6111 which is very close to the theoretical normal distribution probability.

Table 1: Student’s z-scores for their previous and current test grades (n = 18)StudentPrevious Test Scorez-score of Previous Test ScoreCurrent Test Scorez-score of Current Test ScoreIncrease/ DecreaseJonathan931.07890.77DecreaseJamal961.48941.32DecreaseLinda81-0.5881-0.12IncreaseMallorie80-0.7277-0.56IncreaseAmanda941.21910.99DecreaseSabhan880.3880-0.23DecreaseElsa84-0.1779-0.34DecreaseNicole74-1.5468-1.55DecreaseJordan900.66900.88IncreaseLaQuita80-0.7275-0.78DecreaseGrace81-0.58830.10IncreaseMei Wan941.21910.99DecreaseKristin80-0.7269-1.44DecreaseTucker84-0.1781-0.12IncreaseHans77-1.1373-1.00IncreaseJoseph941.21981.76IncreaseIsabella900.66880.66IncreaseAmelia74-1.5470-1.33Increase