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Introduction
The case study involves a bottling company. The main purpose of conducting this research is to investigate concerning the validity of customer’s complaints that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16) ounces of product. Thirty bottles were pulled off the line at random from all the shifts at the bottling plant.
Hypotheses:
H0: The bottle contains less than sixteen (16) ounces.
H1: The bottle contains more than sixteen (16) ounces.
Results of the Calculation
In calculating the mean, the sum of all the data under ounces was divided by the sample size. The mean of the data is 15.27. Median, on the other hand, is the numeric value that separates the higher half of the sample data from the lower half. The median value of the data is 15. Standard deviation is the square root of the data’s variance. The variance of the data set is 0.8242. The square root of 0.8242 is the data’s standard deviation. Hence, the standard deviation is 0.9079.
Confidence interval is a measurement of the reliability of the estimated value. With a sample size of 30, an observed mean of 15.27, and a standard deviation of 0.9079, along with a confidence level of 95%, the confidence interval is +/- 0.32. This means that the bottle contains between 15.68 to 16.32 ounces.
Conclusion
Having calculated the central tendency measures, standard deviation, and confidence interval as well as T-value, it can be concluded that the bottling company has been producing less than 16 ounces of soda in their products. Because of this, the hypothesis that the bottle contains less than 16 ounces is accepted and we reject the alternative hypothesis that the bottle contains equal or more than 16 ounces of soda. To avoid the same deficit in the future, the company must render meticulous inspection of products prior to the distribution in the market.
