You are considering relaxing your control requirements that determine what is acceptable quality; you have been...

You are considering relaxing your control requirements that determine what is acceptable quality; you have been using a 99.0% confidence interval but want to begin using a 97.5% confidence interval.

Your team has collected the following data from 4 samples of 7 observations each. The calculated standard deviation is 13.981.

	Sample 1	Sample 2	Sample 3	Sample 4
Obs 1	392.2	415.1	413.6	399.7
Obs 2	392.3	408.1	394.9	402.3
Obs 3	405.4	428.6	410.1	400.6
Obs 4	410.3	398.2	410.8	427.6
Obs 5	423.3	403.3	423.2	385.8
Obs 6	413.9	421.1	402.7	431.0
Obs 7	426.7	433.5	385.8	405.9

What is the UCL for the mean given the new confidence interval of 97.5%? (Keep one decimal point in your answer)

Solutions

Expert Solution

Following table highlights average values of each sample consisting of 4 samples.

Average value of each sample = Sum of 7 observations / 7

	Sample 1	Sample 2	Sample 3	Sample 4
Observation 1	392.2	415.1	413.6	399.7
Observation 2	392.3	408.1	394.9	402.3
Observation 3	405.4	428.6	410.1	400.6
Observation 4	410.3	398.2	410.8	427.6
Observation 5	423.3	403.3	423.2	385.8
Observation 6	413.9	421.1	402.7	431
Observation 7	426.7	433.5	385.8	405.9
Average =	409.1571	415.4143	405.8714	407.5571

Thus , Xbar = Average of averages = ( 409.1571 + 415.4143 + 405.8714 + 407.5571) /4 = 409.5

Z value for 97.5% confidence interval = NORMSINV ( 0.9875 ) = 2.2414

Given are following data :

Standard deviation = 13.981

Sample size = n = 7 ( since there are 7 observations against each sample )

UCL for the mean given the 97.55 confidence interval

= Xbar + Z x Standard deviation / Square root ( sample size )

= 409.5 + 2.2414 x 13.981 / Square root ( 7 )

= 409.5 + 2.2414 x 13.981 /2.645

= 409.5 + 11.84

= 421.34

UCL FOR MEAN = 421.3

keosha answered 8 months ago

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