Question

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 1 392.2 415.1 413.6 402.2

Obs 2 392.3 408.1 394.9 418.3

Obs 3 405.4 428.6 410.1 419.9

Obs 4 410.3 398.2 410.8 411.6

Obs 5   423.3 403.3 423.2 385.8

Obs 6 413.9 421.1 402.7 431.0

Obs 7 426.7 433.5 385.8 407.1

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

Answer 1

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	402.2
Observation 2	392.3	408.1	394.9	418.3
Observation 3	405.4	428.6	410.1	419.9
Observation 4	410.3	398.2	410.8	411.6
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	407.1
Average =	409.1571	415.4143	405.8714	410.8428

Thus , Xbar = Average of averages = ( 409.1571 + 415.4143 + 405.8714 + 410.8428) /4 = 410.3

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 )

= 410.3 + 2.2414 x 13.981 / Square root ( 7 )

= 410.3 + 2.2414 x 13.981 /2.645

= 410.3 + 11.84

= 422.1

UCL FOR MEAN = 422.1