Calculate SSb and SSwCalculate dfb and dfwCalculate MSb and MSwCalculate FIdentify the critical F-value, compare it to F-observed, and state whether you should accept or reject the null hypothesis. **Analysis of Student Academic Performance Based on Classroom Seating**This study investigates whether the academic performance of students is influenced by their seating position within the classroom. The research involves 30 students who are categorized into three groups based on their seating arrangements: front, middle, and back of the classroom. Each group consists of 10 students, and their final grades at the end of the academic year are recorded.The table below displays the final grades for these students:| | **Front** | **Middle** | **Back** ||----------|-----------|------------|----------|| **Grade**| 72 | 84 | 63 || | 64 | 40 | 71 || | 81 | 77 | 71 || | 90 | 73 | 76 || | 68 | 64 | 44 || | 84 | 71 | 86 || | 53 | 52 | 67 || | 60 | 68 | 75 || | 77 | 78 | 76 || | 79 | 60 | 58 |Summary statistics are provided below each column:- **Total Sum (Σ)**: - Front: 728 - Middle: 667 - Back: 687- **Number of Students (n)**: - All groups: 10**Discussion:**The data showcases the distribution of grades among students sitting in different classroom locations. The total scores for each group are compared to explore potential trends in academic performance relevant to classroom seating. The findings from this study may prompt educators to consider seating arrangements in efforts to optimize student engagement and learning outcomes.

Name: Calculate SSb and SSwCalculate dfb and dfwCalculate MSb and MSwCalcula
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Calculate SSb and SSwCalculate dfb and dfwCalculate MSb and MSwCalculate FIdentify the critical F-value, compare it to F-observed, and state whether you should accept or reject the null hypothesis. **Analysis of Student Academic Performance Based on

Null hypothesis H0: There is no significant difference between academic standing of students who sit closer to and further away from the front of the classroom. Alternative hypothesis Ha: There is a significant difference between academic standing of students who sit closer to and further away from the front of the classroom. Level of significance α = 0.05 = 5% here level of significance is not specified in the question Therefore, choose 5% in general There are three seating positions treated as treatments n1 = number of students in the front = 10 n2 = number of students in the middle = 10 n3 = number of students in the back = 10 N = Total number of observations = n1+n2+n3 = 10+10+10 = 30 k = number of treatments = number of seating positions = 3T1 = Sum of front observations = 728 T2 = Sum of middle observations = 667 T3 = Sum of back observations = 687 G = overall total = T1+T2+T3 = 728+667+687 = 2082 RSS = raw sum of squares =Sum of the squares of all treatments that is 30 observations = 148676 SST = Total sum of squares = RSS - G2N = 148676 - (2082)230 = 148676- 144490.8 = 4185.2 SSb = Sum of squares between treatments = ∑i=13Ti2ni - G2N = (T12n1+T22n2+T32n3) - G2N = ((728)210+(667)210+(687)210) - (2082)230 = 144684.2 - 144490.8 = 193.4 SSw = Sum of squares within the treatments = SST - SSb = 4185.2 - 193.4 = 3991.8 dfb = degrees of freedom for between treatments = k -1 = 3 - 1 = 2 dfw = degrees of freedom for within treatments = N -k = 30 - 3 = 27 MSb = Mean sum of squares between treatments = SSbdfb = 193.42 = 96.7 MSw = Mean sum of squares within treatments = SSwdfw = 3991.827 = 147.8444 To compute F -Ratio, larger of MSb , MSw is taken in the numerator and smaller one is taken in the denominator F - Ratio = MSwMSb = 147.844496.7 = 1.5289 Critical value of F at α = 0.05 = 5% for (N-k, k-1) = (27, 2) d'f can be determined using MS Excel function =FINV(level of significance, df1, df2) =FINV(0.05,27,2) = 19.4587 Conclusion: Observed value of F = 1.5289 > Critical value of F =19.4587 Therefore, reject the null hypothesis that is there is a significant difference between academic standing of students who sit closer to and further away from the front of the classroom.