Asked by Brynleigh Wheeler on Apr 27, 2024
Verified
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 upper control limit?
A) 16.71
B) 2.83
C) 9.77
D) None of the above
Upper Control Limit
The highest value on a control chart that signals when a process is out of control due to variables beyond normal fluctuations.
Sample Means
The average value calculated from a sample of items or individuals, used as an estimate of the population mean.
Basic Statistics
Fundamental principles and techniques used for collecting, analyzing, interpreting, and presenting data.
- Decode control charts and identify what signifies a process as being out of control.
- Determine control limits and understand their significance.
Verified Answer
AG
Alexa GriffithMay 03, 2024
Final Answer :
A
Explanation :
The upper control limit can be found using the formula: UCL = x̄ + 3σ/√n, where x̄ is the mean of the sample means, σ is the standard deviation of the sample means, and n is the sample size (number of students in each class).
Using the given data, we have:
x̄ = 9.77
σ = 2.83
n = 5
Substituting these values into the formula, we get:
UCL = 9.77 + 3(2.83)/√5
UCL ≈ 16.71
Therefore, the value of the upper control limit is approximately 16.71.
Using the given data, we have:
x̄ = 9.77
σ = 2.83
n = 5
Substituting these values into the formula, we get:
UCL = 9.77 + 3(2.83)/√5
UCL ≈ 16.71
Therefore, the value of the upper control limit is approximately 16.71.
Learning Objectives
- Decode control charts and identify what signifies a process as being out of control.
- Determine control limits and understand their significance.