You are considering relaxing your control requirements that determine what is ac
ID: 330076 • Letter: Y
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.
What is the UCL for the mean given the new confidence interval of 97.5%? (Keep one decimal point in your answer)
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 7 426.7 433.5 385.8 405.9Explanation / Answer
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
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
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.