Soda Volumes
Troubleshooting Bottling Errors
Due to customer complaints of low product volume an investigation was conducted to check whether these complaints had any merit. Bottles (n = 30) of soda were randomly taken off the production line and the volumes measured. The total amount of soda measured was ?X = 446.1 oz, so the mean (MX) amount of soda per bottle was ?X/n = 446.1/30 = 14.87 oz. The median value is [(n + 1)/2] = 31/2 = 15.5, so the two middle values were averaged to obtain the median. The two middle values are 14.8 and 14.8, so the median is 14.8. Since the mean and median have similar values, the distribution of soda volumes is not skewed. The standard deviation is SDX = ?{[?(X -- MX) 2]/n-1} = = ?{[(14.5 -- 14.87)2 + (14.6 -- 14.87)2 + . . . + (14.8 -- 14.87)2 + (14.6 -- 14.87)2]/29} = 0.550329.
Calculating the 95% confidence interval (CI) for the data requires determining tcrit, which based on the t table for a two-tailed test with an alpha = .05 would be 2.045. The 95% CI is equal to t (s/?n) = 2.045(0.550329/?30)...
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