1130 The percentage of students classified as disadvantaged

11.30 The percentage of students classified as disadvantaged was compared for samples of schools at three different levels: elementary, middle, and high school. ANOVA was used to compare mean percentages disadvantaged for the three types of school Analysis of Variance Source Factor Error Total sS 5986 23604 29590 MS 2993 315 DF 0.000 75 Individual 95% CIs For Mean Based on Pooled StDev Level N Disadv_e 49 %Disadvm 17 %Disadv.h 12 Mean 70.98 62.72 46.39 StDev----+----+----+- 18.25 18.44 14.09 ( Pooled StDev17.74 48 60 72 a. Suppose students are classified as being economically disadvantaged based on a form that must be completed by parents regarding household income, and sent in to make students eligible for free or reduced school lunch. Explain how this could bring about a difference in reported percentages for the three types of school b. Disadvantaged students might tend to drop out before they have completed high school. Explain how this could bring about a difference in reported percentages for the three types of school c. Which type of school had the highest sample mean? d. Which type of school had the lowest sample mean? e. Are your answers to parts (c) and (d) consistent with your answers to parts (a) and (b)? f. What are the number of groupsI and total sample size N? g. Explain how the degrees of freedom for groups (2) and error (75) could have been calculated from the rest of the output h. Explain how the mean squares, 2,993 and 315, could have been calculated from the rest of the output The F statistic has been blanked out. Use information from the rest of the ANOVA table to report the value of F j. Refer to the P-value in order to choose which two of these conclusions are correct 1. There is no evidence of a relationship between evel of school and percentage of disadvantaged

Solution

f)The number of groups I =49

total sample size=49+17+12=78

g) Since there are 3 levels- %Disadv_e,%Disadv_e,%Disadv_m,%Disadv_h.

So,Factor=3-1=2

Total sample size=78,Total df=78-1=77,

Total df=77,df due to Factor=2,df due to error=77-2=75

h)MS(FACTOR)=SS(FACTOR)/ df due to Factor=SS(FACTOR)/2=5986/2=2993

MS(ERROR)=SSE/df due to error=SSE/75=23604/75=315

i) F=MS(FACTOR)/MSE=2993/315=9.50159