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Statistical Analysis of Soda Bottle Fill Levels: Confidence Intervals and Hypothesis Testing

This analysis applies statistical methods to examine the accuracy of soda bottle fill levels through hypothesis testing.

David Miller
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Statistical Analysis of Soda Bottle Fill Levels: Confidence Intervals and HypothesisTestingAsample of 30 bottles of soda hasbeenrandomly selected from the line and the amount of sodacontained in each of the bottleshasbeenmeasured in ounces. The mean, median and standarddeviation of the amount of soda contained in the bottles have beencalculated from this data.The following table gives the mean, median and standard deviation of the amount of sodacontained in the bottles.Mean14.87Median14.8Standard Deviation0.5503A95% confidence interval for the mean amount of soda contained in the bottlesin ounceshasbeencalculated as follows:The confidence interval for the mean is given as:(x̅−zα2×s√n,x̅+zα2×s√n)Here,SampleSize,n=30Mean,x̅=14.87StandardDeviation,s=0.5503zα2for95%confidence=1.96Thus the95% confidence interval for the meanamount of soda contained in the bottles inouncesis given as:(14.87−1.96×0.5503√30,14.87+1.96×0.5503√30)=(14.87−0.197,14.87+0.197)=(14.673,15.067)Thus, if repeated observations are taken, themeanamount of soda contained in the bottlesisexpected to lie within 14.673 ounces and 15.067 ounces about 95% of the time.Next,a hypothesis testhas beenperformed to verify the claim that a bottle contains less thansixteen (16) ounces of soda.Null and Alternate Hypothesis:Null Hypothesis: The meanamount of soda in the bottles is greaterthan or equal to16 ounces.

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Statistics

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