The mean weight of soda bottles is 15.854 ounces, median weight of soda bottles is 15.99 ounces and standard deviation of soda bottles is 0.661381 ounces. The mean weight infers that the weight of soda bottles is less than 16 ounces whereas the standard deviation of 0.6614 ounces indicates that the spread of weight of soda bottles is insignificant.
We prefer to find confidence intervals of mean weights of soda bottles at 5% level of significance. The upper confidence limit of the mean weight of soda bottles is 16.09 ounces and lower confidence limit of the mean weight of soda bottles is 15.62 ounces
The hypotheses for testing is-
Null hypothesis (H0): The average weight of sampled soda bottles is equal to 16 ounces.
Alternative hypothesis (HA): The average weight of sampled soda bottles is less than 16 ounces.
The calculated t-statistic is (-1.2091).
- At 5% level of significance, the two-tailed t-statistic = 2.04523 (t-critical). As, tcrit>tcal, therefore, we cannot reject the null hypothesis of equality of mean weight of 16 ounces (Lowry, 2014). Hence, there exists the significant equality of weights of soda bottles of 16 ounces.
- From the calculated t-statistic, we find the p-value = 0.236391. As, the p-value is greater than critical p-value that is 0.05, therefore, we accept the null hypothesis of equality of weight of soda bottles 16 ounces. From this approach also, there exists the significant equality of weights of soda bottles of 16 ounces.
From the analysis, it is found that mean weight of 30 soda bottles is less than the expected mean weight. However, it is 95% evident from the hypothesis testing that soda bottle weighs 16 ounces. The claim of consumers is not strongly valid. Although, to minimize spread in terms of standard deviation, we should concentrate on-
- Decrement of the assignable causes arisen of soda factory from manpower and environment
- The correction of error of soda generating machine and weight measuring units (Jiang, 2015).
- Rectification the method of soda generation and retesting the quality of material of soda.
As the spread of the weights of soda bottles would decrease after taking the possible measure, the weights of soda bottles would be very near to 16 ounces (iSixSigma., 2018). Consecutively, the customer satisfaction would increase and reputation of company would be maintained.
It is a topic of concern that as per as the complaint of customers, the weight of soda bottle is less than 16 ounces or not. For examining the complaint of the customers, we have drawn a sample of 30 bottles at random from all the shifting at the bottling plant. The measurements of weights of soda from all the soda bottles are tabulated and used for analysis. After analysing data, we would draw the necessary conclusions.
Common Cause Variation | iSixSigma. (2018). Isixsigma.com. Retrieved from https://www.isixsigma.com/dictionary/common-cause-variation/
Confidence Interval for the Mean. (2018). Onlinestatbook.com. Retrieved from https://onlinestatbook.com/2/estimation/mean.html
Jiang, R. (2015). Product Quality Variations and Control Strategies. In Introduction to Quality and Reliability Engineering (pp. 221-234). Springer, Berlin, Heidelberg.
Lowry, R. (2014). Concepts and applications of inferential statistics.