In: Statistics and Probability
3. The company engineer made adjustments to the filling equipment, including recalibrating the weighers (scales), in an attempt to correct the issue. A random sample of 90 boxes was selected and weighed after the adjustments. The data for this sample can be found in the Excel spreadsheet labeled Weights after Adjustments.
Find the descriptive statistics and the 95% confidence interval for the mean weight of packages after the equipment adjustment. Based on the descriptive statistics and the confidence interval, does it appear that the equipment adjustment had any effect on the weight of the packages? Explain.
below are the numbers in excel:
617.8113 |
620.1644 |
622.8009 |
612.4607 |
623.7648 |
611.1721 |
622.8009 |
613.6156 |
610.1285 |
625.4375 |
619.9092 |
629.9374 |
626.9606 |
622.9659 |
630.2376 |
625.1295 |
614.1246 |
627.8228 |
620.5368 |
616.4157 |
625.8382 |
615.8178 |
628.4465 |
622.1811 |
628.0915 |
613.0679 |
624.8177 |
619.6013 |
627.9645 |
617.9089 |
621.8213 |
620.1643 |
619.8009 |
622.4607 |
623.7648 |
619.1721 |
622.8009 |
617.6155 |
614.1285 |
625.4375 |
619.9092 |
625.9373 |
627.9606 |
619.9659 |
633.2376 |
625.1295 |
612.7446 |
627.8228 |
620.5368 |
617.4158 |
625.8382 |
613.8178 |
628.4465 |
622.1811 |
630.0908 |
611.0679 |
624.8176 |
619.6013 |
627.9645 |
616.9081 |
619.8113 |
620.1643 |
615.8009 |
622.4607 |
623.7648 |
621.1721 |
622.8009 |
613.6156 |
614.1285 |
625.4375 |
619.9092 |
629.9361 |
627.9606 |
619.9659 |
633.2376 |
625.1295 |
618.1246 |
627.8227 |
620.5368 |
611.4159 |
625.8382 |
613.8178 |
628.4464 |
622.1811 |
626.0907 |
613.0678 |
624.8177 |
614.6013 |
629.9645 |
616.9084 |
Using Excel<data<data analysis<descriptive statistics
Descriptive statistics | |
# 1 | |
count | 90 |
mean | 621.615800 |
sample standard deviation | 5.637832 |
sample variance | 31.785151 |
minimum | 610.1285 |
maximum | 633.2376 |
range | 23.1091 |
confidence interval 95.% lower | 620.451033 |
confidence interval 95.% upper | 622.780567 |
margin of error | 1.164767 |
z | 1.96 |
confidence interval 95.% lower | 620.434979 |
confidence interval 95.% upper | 622.796621 |
margin of error | 1.180821 |
t(df = 89) | 1.987 |
1st quartile | 617.664450 |
median | 622.181100 |
3rd quartile | 625.838200 |
interquartile range | 8.173750 |
mode | 622.800900 |
Find the descriptive statistics and the 95% confidence interval for the mean weight of packages after the equipment adjustment. Based on the descriptive statistics and the confidence interval, does it appear that the equipment adjustment had any effect on the weight of the packages?
The 95% confidence interval is (620,623).
Since the confidence interval contains the mean value. We are 95% confident that the population means lies in the confidence interval.