Basic Practice of Statistics (Instructor's)
Basic Practice of Statistics (Instructor's)
8th Edition
ISBN: 9781319057923
Author: Moore
Publisher: MAC HIGHER
Question
Book Icon
Chapter 31, Problem 31.61E
To determine

To calculate: The control limits for s when removing sample 2 and 17. Also add the new control limits to the s chart.

To find: The control limits for x¯ when removing the sample 2 and 17. Make the x¯ chart and comment on the control chart.

Expert Solution & Answer
Check Mark

Answer to Problem 31.61E

For the s chart, the center line is 7.73, the lower control limit is 0 and the upper control limit is 19.85.

Output using the MINITAB software is given below:

Basic Practice of Statistics (Instructor's), Chapter 31, Problem 31.61E , additional homework tip  1

From the s charts, it can be observed that the process is within control.

For the x¯ chart, the center line is 672.95, the lower control limit is 657.8465 and the upper control limit is 688.0535.

Output using the MINITAB software is given below:

Basic Practice of Statistics (Instructor's), Chapter 31, Problem 31.61E , additional homework tip  2

From the x¯ charts, it can be observed that the process is not within control.

Explanation of Solution

Given info:

The data shows the mean and standard deviation for 22 samples of three films.

Calculation:

s chart:

Center line for an s chart:

CL=s¯=(6.8+10.6+12+5.3+4.5+11+6+11.3+8.3+4.1+3.9+6.1+7.9+8.4+6.2+8.3+11.6+5.7+5.8+10.7)20=154.620=7.73

The value of σ^ is

σ^=s¯c4=7.730.8862(From table 31.3, c4=0.8862)=8.72

Upper control limits:

UCL=B6σ^=2.276(8.72)(From table 31.3,B6(=3)=2.276)=19.85

Lower control limits:

LCL=B5σ^=0(8.72)(From table 31.3,B5(=3)=0)=0

Thus, the center line is 7.73, the lower control limit is 0, and the upper control limit is 19.85.

Software procedure:

Step-by-step procedure to construct s charts using the MINITAB software:

  • Choose Graph > Time Series Plot or Stat > Time Series > Time Series Plot.
  • Choose With Groups and click OK.
  • In Series, select the column of standard deviation.
  • In Show reference lines at Y values, enter 0, 7.73 and 19.85.
  • Click OK.

Observation:

Since all observations lie within the lower and upper control limit, the s chart is within control.

x¯ chart:

Center line for a x¯ chart:

CL=x¯¯=¯13,45920=672.95

The value of σ^ is

σ^=s¯c4=7.730.8862(From table 31.3, c4=0.8862)=8.72

Upper control limits:

UCL=x¯¯+3σ^n=672.95+38.723=672.95+15.1035=688.05

Lower control limits:

LCL=x¯¯3σ^n=672.9538.723=672.9515.1035=657.85

Thus, the center line is 672.95, the lower control limit is 657.85 and the upper control limit is 688.05.

Software procedure:

Step-by-step procedure to construct x¯ charts using the MINITAB software:

  • Choose Graph > Time Series Plot or Stat > Time Series > Time Series Plot.
  • Choose With Groups and click OK.
  • In Series, select the column of mean.
  • In Show reference lines at Y values, enter 672.95, 657.85 and 688.05.
  • Click OK.

Observation:

Since all the observations do not lie within the lower and upper control limit, the x¯ chart is not within control.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Using the accompanying Home Market Value data and associated regression​ line, Market ValueMarket Valueequals=​$28,416+​$37.066×Square ​Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram.   LOADING... Click the icon to view the Home Market Value data.       Question content area bottom Part 1 Construct a frequency distribution of the​ errors, e Subscript iei.   ​(Type whole​ numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0   minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5   minus−50005000less than< e Subscript iei less than or equals≤0 21   0less than< e Subscript iei less than or equals≤50005000 9…
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c   Overhead Costs    Billable Hours345000    3000385000    4000410000    5000462000    6000530000    7000545000    8000
Using the accompanying Home Market Value data and associated regression​ line, Market ValueMarket Valueequals=​$28,416plus+​$37.066×Square ​Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet    Market Value1813    911001916    1043001842    934001814    909001836    1020002030    1085001731    877001852    960001793    893001665    884001852    1009001619    967001690    876002370    1139002373    1131001666    875002122    1161001619    946001729    863001667    871001522    833001484    798001589    814001600    871001484    825001483    787001522    877001703    942001485    820001468    881001519    882001518    885001483    765001522    844001668    909001587    810001782    912001483    812001519    1007001522    872001684    966001581    86200
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman