Interpretation: The mean for Diet A (5.341 kg) is slightly greater than twice its standard deviation (5.072 kg), indicating less spread and fewer extreme values. In contrast, Diet B’s mean (3.710 kg) is less than twice its standard deviation (5.538 kg), suggesting greater variability in results. This shows that Diet A was both more effective and more reliable for weight loss compared to Diet B.
Interpretation: The higher median for Diet A suggests better typical outcomes compared to Diet B. While both diets show similar variability, Diet A’s lower IQR indicates slightly more consistency in results. Since the IQR represents the range within which the middle 50% of participants fall, Diet B’s wider IQR suggests a broader spread and potentially less predictability in outcomes.
This analysis reinforces earlier findings that Diet A is both more effective and more consistent than Diet B, offering a stronger case for its recommendation based on both central tendency and dispersion.
Interpretation: Of the 90 respondents in Area 2, 21.1% preferred Brand A, 33.3% preferred Brand B, and the remaining 45.6% preferred some other brand of breakfast cereal. Area 2 shows a more balanced distribution, with Brand B leading and “Others” dropping, suggesting stronger brand loyalty than in Area 1.
Interpretation: The paired t-test assessed whether there was a significant difference in performance between Agent 1 and Agent 2 across 12 batches. With a p-value of 0.0075, which is less than the standard threshold of 0.05, we reject the null hypothesis. This means the difference in means is statistically significant — Agent 2 performed significantly differently from Agent 1.
Interpretation: The independent t-test assessed whether there is a significant difference in mean income between males and females. With a p-value of 0.0014, which is well below the 0.05 significance level, we reject the null hypothesis. This indicates that there is a statistically significant difference in average income between male and female participants in the sample.