Background
As a manager of a bottling company, the claim is that the company’s product (bottled sodas) weighs 16 ounces. The customers however, have complained that the company’s bottled soda does not weigh 16 ounces but instead weighs less than the company’s claim. The boss of the company called for an investigation into this matter and a random sample of 30 bottles from all the shifts of the bottling plant was selected. The weight of the randomly selected bottled sodas was measured and statistical analyses were performed as discussed in the following steps.
Mean, median and standard deviation
The mean, median and the standard deviation for the ounces measured for the 30 randomly selected bottles was calculated using excel and the following results were obtained.
Delegate your assignment to our experts and they will do the rest.
| Column1 | |
| Mean | 15.854 |
| Standard Error | 0.120751098 |
| Median | 15.99 |
| Mode | 16.21 |
| Standard Deviation | 0.661381 |
| Sample Variance | 0.437424828 |
| Kurtosis | 0.559167406 |
| Skewness | -0.792894156 |
| Range | 2.73 |
| Minimum | 14.23 |
| Maximum | 16.96 |
| Sum | 475.62 |
| Count | 30 |
Explanation
From the above table obtained from excel, the mean of the 30 bottled sodas was found to be 15.854 ounces and a standard deviation of 0.661381. This means that on average the weight of a randomly selected bottle will be 15.85 ounces or approximately 16 ounces when rounded off to the nearest whole number. The standard deviation is the square root of the variance and it shows how much different weights vary from the mean. In this case, the bottled sodas weight deviates by 0.66 ounces from the mean weight. The calculated median value was found to be 15.99 and the mode which shows the most repeated weight value was found to be 16.21.
A 95% Confidence Interval for the ounces in the bottles.
The confidence interval is a range of values in which the true value of a population parameter lies. The company was interested in finding the 95% confidence level of the weights of the selected products and the analysis was conducted using excel software to obtain the following results.
| Column1 | |
| Mean | 15.854 |
| Standard Error | 0.120751098 |
| Median | 15.99 |
| Mode | 16.21 |
| Standard Deviation | 0.661381 |
| Sample Variance | 0.437424828 |
| Kurtosis | 0.559167406 |
| Skewness | -0.792894156 |
| Range | 2.73 |
| Minimum | 14.23 |
| Maximum | 16.96 |
| Sum | 475.62 |
| Count | 30 |
| Confidence Level (95.0%) | 0.246963724 |
The 95% confidence level value was obtained as 0.24696. The confidence interval is given by [15.607 < 15.854 < 16.101] i.e. (15.854-0.24696 = 15.60703628) and (15.854+0.24696= 16.10096372). This implies that the company can be 95% confident that the weight of their bottled soda is between 15.6 ounces and 16.1 ounces. Therefore, if more surveys are to be done in future, then 95% of them would result in confidence intervals that include the true population proportion.
Hypothesis Test
In order to test the claim made by the customers that the weight of the bottled sodas is less than 16 ounces, a hypothesis test was conducted. Since the data collected had a sample size of 30 and there was no population standard deviation given, a one sample t-test was conducted in order to test the claim that the weight is less than 16 ounces. The null and the alternative hypothesis were formulated as follows.
H 0 : µ=16
H 1 : µ<16
The following one-sided t-test was obtained from excel.
| t-Test: one sample | |
| Ounces | |
| Mean | 15.854 |
| Variance | 0.437424828 |
| Observations | 30 |
| Hypothesized Mean | 16 |
| df | 29 |
| t Stat | -1.20909874 |
| P(T<=t) one-tail | 0.118195315 |
| t Critical one-tail | 1.699127027 |
| P(T<=t) two-tail | 0.23639063 |
| t Critical two-tail | 2.045229642 |
Analysis
The t statistic value obtained was -1.209 with a p value of 0.1182. The null hypothesis is only rejected when the t stat value is greater than the tabulated value but in this case, the t stat value is -1.209 and the tabulated value from the student t distribution table is 1.699. This implies that t calculated (-1.209) is less than t tabulated (1.699) therefore, the null hypothesis is not rejected.
The null hypothesis therefore is true and the conclusion is that, the company’s claim that the weight of the bottled sodas has a mean weight of 16 ounces holds. In other words, it is true the product has a weight of 16 ounces as advertised and the customer’s complaints are not warranted.
Recommendation
From the statistical analysis conducted above, it is clear that the customer’s complaints are not justified. I would assume that the customers are made to believe that our products are less than what is advertised because of our packaging material. When comparing our bottled products to other companies, ours seem lighter due to our plastic packaging material. I would strongly suggest therefore, that we change our packaging material to cans or even glass bottles as they weigh slightly more than plastic. This, I believe, would restore our customer confidence.
