Homework SourseA machine that stuffs a cheesefilled snack product can be ad
A machine that stuffs a cheese-filled snack product can be adjusted for the amount of cheese injected into each unit. A simple random sample is selected and the average amount of cheese injected is found to have a sample mean of 3.5 grams. The process standard deviation for the population is known to be 0.25 grams. Below, complete the table for three levels of confidence, 90%, 95% and 99%, for sample sizes 10, 20, 30, …, 100. Hint: Excel has a worksheet function CONFIDENCE that can be used to determine the half-width of the confidence intervals when the population standard deviation is known. The syntax is: CONFIDENCE(,,n) where = 1 – confidence level (e.g., 0.05 for 95% confidence intervals). Average = 3.5 StDev = 0.25 n = Half Interval LCL, 90% UCL, 90% Half Interval LCL, 95% UCL, 95% Half Interval LCL, 99% UCL,99% 10 20 30 40 50 60 70 80 90 100 How are the limits of the confidence intervals affected by the change in confidence level? How are the limits of the confidence intervals affected by the change in sample size?
Solution
Sample size
90%
90%
95%
95%
99%
99%
LCL
UCL
LCL
UCL
LCL
UCL
10
3.370
3.630
3.345
3.655
3.296
3.704
20
3.408
3.592
3.390
3.610
3.356
3.644
30
3.425
3.575
3.411
3.589
3.382
3.618
40
3.435
3.565
3.423
3.577
3.398
3.602
50
3.442
3.558
3.431
3.569
3.409
3.591
60
3.447
3.553
3.437
3.563
3.417
3.583
70
3.451
3.549
3.441
3.559
3.423
3.577
80
3.454
3.546
3.445
3.555
3.428
3.572
90
3.457
3.543
3.448
3.552
3.432
3.568
100
3.459
3.541
3.451
3.549
3.436
3.564
With increase in confidence levels the limits decrease. In each row we observe the values of LCLs are decreasing and UCLs are decreasing
With increase in sample size the limits increase.
| Sample size | 90% | 90% | 95% | 95% | 99% | 99% |
| LCL | UCL | LCL | UCL | LCL | UCL | |
| 10 | 3.370 | 3.630 | 3.345 | 3.655 | 3.296 | 3.704 |
| 20 | 3.408 | 3.592 | 3.390 | 3.610 | 3.356 | 3.644 |
| 30 | 3.425 | 3.575 | 3.411 | 3.589 | 3.382 | 3.618 |
| 40 | 3.435 | 3.565 | 3.423 | 3.577 | 3.398 | 3.602 |
| 50 | 3.442 | 3.558 | 3.431 | 3.569 | 3.409 | 3.591 |
| 60 | 3.447 | 3.553 | 3.437 | 3.563 | 3.417 | 3.583 |
| 70 | 3.451 | 3.549 | 3.441 | 3.559 | 3.423 | 3.577 |
| 80 | 3.454 | 3.546 | 3.445 | 3.555 | 3.428 | 3.572 |
| 90 | 3.457 | 3.543 | 3.448 | 3.552 | 3.432 | 3.568 |
| 100 | 3.459 | 3.541 | 3.451 | 3.549 | 3.436 | 3.564 |
