Question

**S6.23' The school board is trying to evaluate a new math program introduced to second-graders in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the fol- lowing data: SCHOOL NO, OF TEST ERRORS 35 55 Construct a c-chart for test errors, and set the control limits! to contain 99.73% of the random variation in test scores What does the chart tell you? Has the new math program been effective PX

Answer 1

s toying heord he school to ealuate SG. 23 a neuw inta odured to Second gaaden in ftve math A Sample elevnentnrg Scheols the county this acooss on slanda ndiz ed math teste of the students godes falasin dola each elomentad shool yleld n c chant school wise dos eaoos onstoret calculate t avesaage fast numben of test eootoos Sheson belo as School Alamadecor est eao A 52 27 35 55 Tolal 213 u2.6 tegt esurasT42.6 numbea Oeora ge

GNen z3 o .431. Conft dence level Compule e ppeo Conool mit and ucl c E3x UcLc (2) C3 xJE Lcle ere ts numben o test eoooos. he avooe Substtule 42.6 to delain ucle n Equaion c) e Value of Uche 42.6 +3x Jus.6 u2.6 3*6.53 42. 6t \a.5e 62.19 te Condool mit vcLe 62.18 uppea u2.6 to obain Le in Equation (2), tevaue of sakslitute 42.6 3 x Ju Lele 42.63x 6.53 42.6 23.02 lowren Contool mtt Lele = 23-01

UCL 62.18 and Plot the school wise test errors in the c chart given the values of 42.6 23.02. The upper control chart limits and lower control chart limits are shown in red LCL = 42.6 value is shown in green colour. colour. The 65 60 UCL-62.18 55 E, 55 50, A, 52 45 C 42.6 D44 40 35 С, 35 30 LCL 23.02 25 B.27 20 As per the chart, the school wise test errors are within the control limits. Two of the schools A and E have the number of test errors" higher than the average and they are also close to the upper control limit Perhaps more data would be required to judge the effectiveness of the new programme.