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ECON2142 - Statistical Decision Making and Quality control

   

Added on  2020-03-04

4 Pages510 Words31 Views
Student name: Student number:Subject code:Subject name:Assignment Due date:Return date:Submission method 1
ECON2142 - Statistical Decision Making and Quality control_1
Student name: Student number:QUESTION 3 Statistical Decision Making and Quality Control The following formulas are used to find the upper control limit UCL, and lower control limit LCL,[ CITATION Mon03 \l 1033 ]UCL=mean-Z*StDev/sqrt(n)LCL=mean+Z*StDev/sqrt(n)Where mean is the sample mean (20), StdDev is the population standard deviation (10), n is the given size of the sample which will be changing for different parts of the problem, and Z represents the critical value (as obtained from Z table) according to the given level of confidence which will change in different parts of the problem In what follows, we substitute in the above formula1.95% of confidence with Samples of 64 observations :LCL=20-1.96*10/ sqrt (64)= 17.55UCL=20+1.96*10/sqrt(64)= 22.452.95% of confidence with 16 observations LCL= 20-1.96*10/ sqrt (16)= 15.1UCL= 20+1.96*10/ sqrt (16)= 24.93.In this part we investigate how the level of confidence and sample size will affect the calculation of the confidence interval, more specifically the effect on the interval width.Increasing the sample size to 16 observations and setting confidence level to 90%L= 20-1.645*10/ sqrt( 16)= 15.8875U= 20+1.645*10/ sqrt(16)= 24.1125Keeping the confidence level at 95% and upraising the sample size to 64 observationsL = 20-1.96*10/ sqrt(64)= 17.55U=20+1.96*10/ sqrt(64)= 22.45Holding the confidence level at 95% while reducing the sample sizes of to 36 observations.L= 20-1.96*10/ sqrt(36)= 16.73333U= 20+1.96*10/ sqrt(36)= 23.266672
ECON2142 - Statistical Decision Making and Quality control_2

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