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# Statistical applications

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Statistical applications continue to stimulate corporate progress around the world. Every firm wants to have the best items on the market in order to retain current consumers and attract new ones. Superior products, on the other hand, necessitate strict decision-making guidelines for the organization. Quality control is an important guideline in ensuring that products meet the criteria or standards of the client. Subpar products can have a significant influence on a company's consumer base and overall performance. The paper is a case study of a bottling plant, with the goal of determining if the filling process achieves the set criteria of 16 ounces of soda each bottle. The case study was motivated by complains from some of the customers that there was less soda in the bottles than advertised by the company. The data collection involves a cross-sectional process where a random sample of the bottles filled with soda by the where pulled from line across by all working shifts by the employees. The statistical analysis involved both descriptive and inferential methods.

Statement of hypotheses:

Null hypothesis: There are sixteen ounces of soda in each of the bottles.

Alternative hypothesis: The bottles contain less than sixteen ounces of soda.

Results of Data Analysis

The mean, median, and standard deviation for the number of ounces in sample of bottles

Table .1 Summary statistics of the ounces in the bottles

Statistic

Value (ounces)

Mean

15.854

Median

15.99

Standard Deviation

0.661381

From Table 1 above, the summary statistics from the sample of thirty bottles from the line indicate a mean value of 15.854 ounces and the median is 15.99 ounces of soda. The standard deviation indicates that average variation of a given bottle from the mean value is 0.661 ounces.

The 95% Confidence Interval for the mean value of ounces

The population standard deviation of the production line is unknown; this implies that the confidence interval will be calculated using t-statistic. The formula for calculation is as given below.

Where the sample mean, t is the critical value =2.045, s is the sample standard deviation, and n is the sample size.

Confidence intervals

Therefore, the confidence interval explains that the actual mean value of soda in the bottle falls between 15.607 ounces 16.101 ounces.

Testing claim that a bottle contains less than sixteen (16) ounces

Testing the hypothesis

The above stated hypotheses are tested at the 0.05 level of significance. The decision criterion: Reject the null hypothesis if test-statistic is greater than the critical value.

The test statistic for one sample t-test

The test statistic is obtained by calculating the student t–distribution value as provide in the formula below.

Where t is test statistic, mu is the population average or the hypothesized mean for bottle ounces. The test statistic is:

The t-statistic is -1.209. Since |t-stat| < 1.699, we cannot reject the null hypothesis that the bottles produced have 16 ounces. This implies the customers are not substantiated.

In conclusion, the customer’s claims that the company is producing substandard soda bottles are not substantiated. The company does not need to change the current bottling line. However, the company can try to reduce elements that introduce extraneous variation in the lines. The dispatch department needs to check bottles prior to releasing them into the market.

May 17, 2023
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