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

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Statistical Analysis of Soda Bottle Fill Levels: Confidence Intervals and Hypothesis Testing A s ample of 30 bottles of soda has been randomly selected from the line and the amount of soda contained in each of the bottles has been measured in ounces. The mean, median and standard deviation of the amount of s oda contained in the bottles have been calculated from this data. The following table gives the mean, median and standard deviation of the amount of soda contained in the bottles. Mean 14.87 Median 14.8 Standard Deviation 0.5503 A 95% confidence interval for the mean amount of soda contained in the bottles in ounces has been calculated as follows: The confidence i nterval for the mean is given as : ( x ̅ − z α 2 × s √ n , x ̅ + z α 2 × s √ n ) Here , Sample Size , n = 30 Mean , x ̅ = 14 . 87 Standard Deviation , s = 0 . 5503 z α 2 for 95% confidence = 1 . 96 Thus the 95% confidence interval for the mean amount of soda contained in the bottles in ounces is 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, the mean amount of soda contained in the bottles is expected to lie within 14.673 ounces and 15.067 ounces about 95% of the time. Next, a hypothesis test has been performed to verify the claim that a bottle contains less than sixteen (16) ounces of soda. Null and Alternate Hypothesis: Null Hypothesis: The mean amount of soda in the bottles is greater than or equal to 16 ounces .
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