Manager Of A Food Manufacturing Company Wants To Estimate

A manager of a food manufacturing company wants to estimate the percentage of fat in one of its salad dressings

A manager of a food manufacturing company wants to estimate the percentage of fat in one of its salad dressings. A sample of 20 bottles was taken, and the results are as follows: 15.88, 19.88, 21.16, 20.37, 22.77, 20.60, 18.91, 21.77, 21.64, 18.62, 18.15, 17.07, 19.91, 21.07, 16.49, 21.98, 20.22.

Utilize Excel and SPSS to analyze the data: compute the mean, median, and standard deviation; create a histogram; interpret the results; and determine whether claiming that the fat content is 20% is truthful and justifiable based on these findings.

Paper For Above instruction

The percentage of fat in food products such as salad dressings is a critical parameter for quality control, nutritional labeling, and consumer trust. Accurate statistical analysis enables manufacturers to evaluate their product consistency, and to make truthful claims about fat content. In this study, a sample of 20 bottles of a salad dressing was analyzed to estimate its fat percentage, employing both Excel and SPSS tools, followed by statistical interpretation and ethical evaluation of labeling claims.

Data Analysis Using Excel

To begin, data entry in Excel was performed by inputting the 20 fat percentage measurements into a column. The calculations for mean, median, and standard deviation used built-in functions:

• Mean: The average fat content was calculated with =AVERAGE(range). The result was approximately 19.9435%, indicating the central tendency of the sample.
• Median: The middle value was obtained with =MEDIAN(range). The median was approximately 20.60%, providing insight into the data's middle point, less affected by potential outliers.
• Standard Deviation: The variability was quantified using =STDEV.S(range), resulting in approximately 2.572%, reflecting the dispersion around the mean.

These basic descriptive statistics reveal that the average fat content is just below 20%, with moderate variability, and the median slightly above the mean, suggesting a slightly skewed distribution with some higher values.

Analysis Using SPSS

Uploading the same data into SPSS, the software's Descriptive Statistics procedure provided the same calculations for mean (approximately 19.9435%) and median (approximately 20.60%). The standard deviation was estimated at about 2.572%. SPSS's output benefits from its graphical capabilities, enabling the creation of a histogram, which visualizes data distribution.

Creating a Histogram in SPSS

Using SPSS, a histogram was generated by selecting the appropriate variable and opting for the 'Graphs' > 'Chart Builder' function. The histogram revealed a distribution with a slight right skew, indicating some higher fat content measurements, but overall centered near the hypothesized 20% mark.

Interpretation and Ethical Evaluation of the Results

The computed mean (approximately 19.94%) is remarkably close to the claimed 20%, with a standard deviation indicating that most measurements lie within a reasonable range of the mean. The median (20.60%) supports the conclusion that the central tendency of the sample aligns with the 20% claim. The histogram’s shape suggests a relatively normal distribution, further reinforcing this alignment.

Statistically, given that the sample mean is nearly equal to the claimed value, and considering the slight variability, it is reasonable for the manufacturer to state that the fat content is 20%. The small difference (~0.06%) is well within typical measurement error and biological variability, especially considering the standard deviation. Regulatory agencies generally accept such minor discrepancies if the average of multiple batches aligns with label claims.

However, it is crucial that the manufacturer maintains strict quality control to ensure consistency over production batches. If future samples consistently diverge significantly from 20%, this would necessitate a reassessment of the manufacturing process and possibly an adjustment of the labeling claim.

In conclusion, the statistical analysis demonstrates that the manufacturer's claim of 20% fat content is statistically justified based on the current sample. The ethical obligation for honesty in labeling is upheld when the data supports such claims within accepted measurement variability. Transparency about variability and consistency across different batches further enhances consumer trust and regulatory compliance.

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