Presentation of the data: For charter schools: Math Test Average CHARTER SCHOOLS cumulative upper lower midpoint frequency percent frequency percent 165 < 175 170 0 0.0 0 0.0 175 < 185 180 0 0.0 0 0.0 185 < 195 190 4 9.1 4 9.1 195 < 205 200 5 11.4 9 20.5 205 < 215 210 7 15.9 16 36.4 215 < 225 220 5 11.4 21 47.7 225 < 235 230 4 9.1 25 56.8 235 < 245 240 4 9.1 29 65.9 245 < 255 250 3 6.8 32 72.7 255 < 265 260 5 11.4 37 84.1 265 < 275 270 7 15.9 44 100.0 44 100.0 Descriptive statistics Charter Schools Math Test Average count 44 mean 230.4318 sample variance 756.9813 sample standard deviation 27.5133 minimum 187.8 maximum 274.3 range 86.5 NJ Charter High Schools Math Scores 16 8 4 99 5 27 4. 26 5 25 5 24 5 23 5 22 5 21 5 20 5 19 5 18 5 17 5 0 16 Percent 12 Math Test Average For non- charter schools: Math Test Average NON-CHARTER SCHOOLS cumulative upper lower midpoint frequency percent frequency percent 165 < 175 170 0 0.0 0 0.0 175 < 185 180 3 6.4 3 6.4 185 < 195 190 3 6.4 6 12.8 195 < 205 200 1 2.1 7 14.9 205 < 215 210 6 12.8 13 27.7 215 < 225 220 12 25.5 25 53.2 225 < 235 230 12 25.5 37 78.7 235 < 245 240 7 14.9 44 93.6 245 < 255 250 3 6.4 47 100.0 Descriptive statistics Non-charter Schools Math Test Average count 47 mean 221.2213 sample variance 318.5769 sample standard deviation 17.8487 minimum 176 maximum 248.3 range 72.3 NJ Non-Charter High Schools Math Scores 30 15 8 99 25 4. 5 24 5 23 5 22 5 21 5 20 5 19 5 18 5 17 5 0 16 Percent 23 Math Test Average 47 100.0 Hypothesis test: Ho: C NC or C - NC 0 HA: C > NC or C - NC > 0 Tcrit = 2.416 ( using = 0.01 in one tail and df = n - 1 = 44 - 1 = 43 using the smaller of the sample sizes) In Excel, t.inv(.99,43) t* = t* = x1 x2 2 s12 s2 + n1 n2 230.43 221.22 27.512 17.85 2 + 44 47 = 1.681 Fail to reject Ho. The 9.21 point difference between the mean math test score for charter high schools and non-charter high schools is not sufficient evidence to prove that the charter schools have significantly higher math scores than non-charter schools, on average. There was quite a bit of variation within the two data sets which resulted in me not being confident in the difference I found between the two means. In particular there was a very large amount of variation within the charter school group. Looking at the graphs, one can see that there were several outliers in the left tail of the non-charter school distribution that brought their mean down while there were 7 charter schools that scores higher than any of the public schools and yet their average was still not that much higher than the non-charter school average. It seems that while the mean math score was not found to be significantly higher, there is a great amount of variation in the charter schools than in the noncharter schools. Survey Score R Survey Score NR 5.4 5.1 5.0 5.0 5.3 5.7 4.1 5.5 5.3 5.2 5.5 4.9 5.2 5.5 4.9 5.1 5.1 4.7 5.3 5.7 5.5 5.0 5.2 5.4 5.0 4.9 5.1 5.4 5.6 5.2 5.2 5.0 3.8 5.3 5.0 4.5 4.4 4.6 4.7 5.0 4.9 5.0 5.3 5.0 4.7 5.5 4.0 4.4 5.2 4.5 5.1 4.1 5.0 5.4 3.9 4.8 5.2 4.0 5.1 4.9