Bottling Company the Mean, Median and Standard

Bottling Company

The mean, median and standard deviation are as follows:

Bottle No.

Oz

mean median std dev

The 95% confidence interval can be calculated as follows:

CI = x +/- t* (s/?n)

CI = 14.87 +/- 2.045 * (0.541 / ?30)

CI = 14.87 +/-

CI = 14.668 to 15.07

The null hypothesis is that the bottles are within the 95% confidence interval of 16oz as required by law. So the number of samples that fall within 15.8 to 16.2. This reality is that there are only three that fall within this, which shows that the null hypothesis is rejected. The samples deviate far too much from the desired 16 ounce state.

There are clearly less than 16 ounces of soda in each bottle. There are a number of possible causes for this. We have to first look at the measurement, to ensure that the device is measuring things properly. This is not always the case. The equipment is sometimes faulty. In this instance, the mean is closer to 15 ounces than 16 ounces, which might call into question the measuring capabilities of the equipment. That is worth looking into.

The second possibility is that the machine is simply not putting enough soda into the bottles. This is an issue with the calibration of the dispensing machine, rather than with the calibration of the measuring machine. In this case, it is fairly evident if the measuring device tests fine that the calibration machine is off a little bit, and the bottles are not being filled to the 16 ounce capacity. The result of this is that the consumer has a reasonable complaint and that the liquid is simply not getting into the bottles in the first place.

I'm not entirely sure what the third possibility would be. Either the measurement is off or the amount of liquid is off -- I'm curious what the third option might be here. It seems that there could not be too many other options available.

To avoid the problem in the future requires dealing with whichever is the major problem here. It is reasonable to assume that with two possible problems, the solution lies with identifying which of the possible problems is the issue and just dealing with that. So the problem can be addressed as follows. If the issue is that the measures are off, then the measuring devices need to be recalibrated. If the issue is that the filling device is off, then the filling device needs to be recalibrated. Clearly, some third party equipment that has been independently calibrated will be needed, in order to define the parameters by which we are measuring. But at the end of the day, the critical factor is that once all of the devices have been recalibrated, the problem should be solved and no more will there be issues with underfilling of bottles.