Question

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 following data: School No. of Test Errors A 52 B 27 C 35 D 44 E 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?

Answer 1

Answer:

a) The chart tell us that all the point are between the upper and lower control limits, so the process is under control.

b) Since the process under control, the number of defects are controled and we know with a 99.3 % of certainty the average of them, so the program is  effective.

Explanation:

In order to draw a C chart we should calculate the  average test errors and the control limits of the chart

The average test errors is = (52+27+35+44+55)/5= 42.6 = c

This will be the middle line in the chart.

Then, the Upper and lower control limits are:

LCL=  c-m *sqr(c) and UCL= c+ m *sqr(c)

In this case, since we are told to contain the 99,7% of random variation, this means that we are working with a 6 sigma.

So m will be 3 (3 sigma) for the upper limit control and 3 (3 sigma) for the lower limit control:

LCL= 42.6 -3*sqr(42,6) = 23.0

UCL= 42.6+3*sqr(42,6) = 62.2

(the graphic is attached)

As we can see, al the test error values are between the control limits, so the program is undercontrol

Download xlsx