In the packaging process, equipment is set to fill boxes with a mean weight of 20.2 ounces. This is the standard for the population. Population standard deviation is not known.
1. Calculate a 95% confidence interval for the mean weight of the cereal boxes, using the sample data
Package Weights |
21.295 |
21.296 |
19.816 |
19.885 |
20.211 |
20.212 |
20.304 |
20.306 |
20.313 |
20.465 |
20.468 |
20.468 |
20.722 |
20.723 |
20.724 |
20.483 |
20.484 |
20.485 |
20.64 |
20.64 |
20.646 |
20.649 |
19.199 |
19.988 |
20.213 |
20.225 |
20.245 |
20.222 |
20.6 |
20.599 |
20.61 |
20.94 |
20.94 |
20.153 |
20.16 |
20.939 |
20.943 |
20.819 |
20.816 |
20.819 |
20.226 |
20.227 |
20.223 |
20.591 |
20.592 |
20.592 |
20.593 |
20.588 |
20.315 |
20.311 |
20.316 |
20.316 |
20.251 |
20.33 |
20.331 |
20.332 |
20.424 |
20.425 |
20.425 |
19.228 |
19.695 |
20.894 |
20.898 |
20.896 |
20.243 |
20.244 |
20.244 |
20.642 |
20.642 |
20.643 |
20.643 |
20.333 |
20.334 |
20.352 |
20.942 |
20.947 |
20.948 |
20.949 |
20.419 |
20.421 |
20.421 |
20.423 |
20.423 |
20.746 |
20.747 |
20.748 |
20.386 |
20.382 |
20.612 |
20.611 |
20.613 |
20.609 |
19.232 |
19.983 |
19.984 |
20.374 |
20.374 |
20.384 |
21.145 |
21.172 |
21.177 |
21.178 |
20.618 |
20.619 |
20.364 |
20.368 |
20.434 |
20.435 |
20.566 |
20.584 |
20.589 |
20.903 |
20.469 |
20.469 |
20.471 |
20.905 |
20.906 |
20.445 |
20.443 |
20.949 |
20.951 |
20.969 |
20.369 |
20.37 |
20.37 |
20.37 |
20.834 |
20.845 |
20.847 |
20.84 |
20.666 |
20.666 |
20.667 |
20.428 |
20.431 |
20.635 |
20.636 |
20.636 |
20.637 |
20.529 |
20.533 |
20.534 |
20.23 |
20.233 |
20.242 |
20.243 |
19.985 |
19.187 |
19.986 |
19.987 |
20.463 |
20.465 |
20.792 |
20.799 |
20.806 |
20.818 |
20.463 |
20.525 |
20.529 |
20.529 |
19.989 |
20.151 |
20.151 |
20.654 |
20.655 |
20.657 |
20.661 |
20.354 |
20.36 |
20.362 |
20.5 |
20.508 |
20.512 |
20.876 |
20.876 |
20.867 |
20.495 |
20.497 |
20.498 |
20.162 |
20.162 |
20.164 |
20.99 |
20.21 |
20.629 |
20.63 |
20.632 |
20.493 |
20.492 |
20.491 |
20.246 |
20.258 |
20.259 |
20.26 |
20.447 |
20.527 |
20.519 |
20.527 |
20.526 |
20.528 |
20.48 |
20.481 |
20.723 |
20.726 |
20.725 |
20.451 |
20.453 |
20.456 |
20.462 |
20.623 |
20.624 |
20.625 |
20.626 |
20.517 |
20.527 |
21.289 |
21.29 |
20.651 |
20.652 |
20.541 |
20.634 |
20.635 |
20.499 |
20.499 |
20.719 |
20.719 |
20.72 |
20.721 |
20.493 |
20.494 |
20.494 |
20.496 |
20.495 |
20.627 |
20.511 |
20.524 |
20.526 |
20.628 |
20.629 |
20.59 |
20.534 |
20.535 |
20.536 |
20.537 |
20.878 |
20.878 |
20.878 |
20.881 |
20.652 |
20.653 |
20.727 |
20.482 |
20.483 |
20.48 |
20.729 |
20.729 |
20.621 |
20.622 |
20.622 |
20.595 |
20.597 |
20.598 |
20.644 |
20.64 |
19.696 |
19.697 |
20.882 |
20.88 |
20.639 |
20.246 |
20.258 |
20.259 |
20.639 |
20.785 |
20.787 |
20.565 |
20.556 |
20.558 |
20.567 |
20.651 |
20.637 |
20.638 |
20.638 |
20.487 |
20.486 |
20.776 |
20.777 |
20.778 |
20.778 |
20.65 |
20.651 |
20.397 |
20.397 |
20.399 |
20.419 |
20.418 |
20.667 |
20.668 |
20.67 |
20.371 |
20.373 |
20.372 |
20.736 |
20.74 |
20.74 |
20.742 |
20.656 |
20.653 |
20.653 |
20.665 |
20.847 |
20.849 |
20.526 |
20.526 |
20.517 |
20.874 |
20.671 |
20.672 |
20.672 |
20.674 |
20.673 |
20.676 |
20.702 |
20.514 |
20.509 |
20.515 |
20.426 |
20.422 |
20.426 |
20.426 |
20.426 |
20.427 |
20.617 |
20.62 |
20.428 |
20.429 |
20.435 |
20.437 |
20.437 |
20.442 |
20.713 |
20.753 |
20.75 |
20.64 |
20.641 |
20.73 |
20.91 |
20.911 |
20.934 |
20.936 |
20.73 |
20.388 |
20.389 |
20.594 |
20.594 |
20.395 |
20.396 |
21.061 |
20.887 |
20.883 |
21.179 |
21.18 |
20.738 |
19.698 |
19.812 |
20.717 |
20.718 |
20.695 |
20.696 |
20.697 |
20.769 |
20.769 |
20.771 |
20.922 |
20.909 |
20.919 |
20.771 |
20.774 |
20.224 |
20.229 |
20.231 |
20.231 |
20.682 |
20.694 |
20.694 |
20.904 |
20.912 |
20.907 |
20.448 |
20.45 |
20.452 |
20.884 |
20.885 |
20.888 |
20.79 |
20.791 |
20.352 |
20.353 |
20.355 |
20.787 |
20.788 |
20.944 |
20.941 |
20.942 |
20.152 |
20.153 |
20.659 |
20.653 |
20.658 |
20.822 |
20.823 |
20.789 |
20.789 |
21.287 |
21.288 |
20.162 |
20.821 |
20.821 |
20.302 |
20.304 |
20.301 |
20.831 |
20.832 |
20.833 |
21.144 |
21.146 |
21.145 |
20.824 |
20.83 |
20.938 |
20.939 |
20.755 |
20.937 |
20.928 |
20.929 |
20.857 |
20.875 |
20.876 |
20.673 |
20.361 |
20.362 |
20.677 |
20.675 |
20.679 |
20.877 |
20.878 |
20.907 |
20.907 |
20.908 |
20.26 |
20.261 |
20.261 |
20.886 |
20.893 |
20.892 |
21.292 |
21.293 |
21.294 |
20.749 |
20.23 |
20.91 |
20.761 |
20.762 |
20.768 |
21.063 |
21.065 |
21.143 |
20.756 |
20.757 |
20.759 |
20.981 |
20.987 |
20.988 |
20.664 |
20.662 |
20.975 |
20.977 |
20.541 |
20.542 |
20.543 |
20.544 |
20.989 |
20.731 |
20.732 |
20.733 |
20.679 |
20.68 |
20.681 |
21.283 |
20.709 |
20.712 |
20.713 |
20.974 |
20.976 |
19.813 |
19.814 |
21.053 |
21.063 |
20.759 |
20.76 |
2. Based on the confidence interval for the mean weight of cereal boxes, does this sample provide evidence that the packaging process is meeting the company standard? Explain.
1. For given data of size n=500, and
Margin of Error=
Hence
2. As 20.2 is not in range this is not meeting the company standard
In the packaging process, equipment is set to fill boxes with a mean weight of 20.2...