The data below represent the means from 15 sample control charts for the amount of time in minutes it takes students to complete a quiz in a basic statistics course.The same quiz was given to 15 different sections of a basic statistics course.Five students were sampled from each class and each mean is shown below. What is the value of the lower control limit?
A)16.71
B)2.83
C)9.77
D)None of the above

Question

The data below represent the means from 15 sample control charts for the amount of time in minutes it takes students to complete a quiz in a basic statistics course.The same quiz was given to 15 different sections of a basic statistics course.Five students were sampled from each class and each mean is shown below.  What is the value of the lower control limit?
A)16.71 
B)2.83 
C)9.77 
D)None of the above

Quizplus · Accepted Answer

To calculate the lower control limit for an X̅ chart, we use the formula:

LCL = X̄ - 3s/√n

where X̄ is the overall mean of the sample means, s is the standard deviation of the sample means, and n is the sample size (in this case, n = 5). Using the given data, we can calculate:

X̄ = 9.77 (the mean of the 15 sample means)
s = 3.27 (the standard deviation of the 15 sample means)
LCL = 9.77 - 3(3.27)/√5 ≈ 2.83

Therefore, the value of the lower control limit is approximately 2.83.

The Data Below Represent the Means from 15 Sample Control