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 65 14 36 D 55 For the test errors, the o-chart with controllimits that contain 99.73% of the random variation in test scores is: UCL, -errors (round your response to two decimal places) LOL, -erron (round your sponse to two decima places and if your answer is negative, and the value os a), According to the chart, there are schools out of control NO SOME

Answer 1

Mean Number of test errors ($\bar {c}$) = (65 + 14 +36 + 43 + 55) / 5 = 42.6

The upper and lower control limits in control chart is given by

$UCL_c=\bar {c}+z\sqrt{\bar {c}}$

$LCL_c=\bar {c}-z\sqrt{\bar {c}}$

For control limits containing 99.73% of the random variation, $z=3$

=> $UCL_c=42.6+3*\sqrt{42.6}=62.18$

and, $LCL_c=42.6-3*\sqrt{42.6}=23.02$

School A is out of upper control limit and School B is below lower control limit.

Hence, According to the c-chart, there are SOME schools out of control.