Assignment 3 STAT2040

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Toronto Metropolitan University *

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Statistics

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Feb 20, 2024

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Uploaded by SargentEnergy8424

Part A:A Bit on t-Tests The value of the t-test statistic I obtained is -2.5737 and my p-value is 0.9898. We would fail to reject the null hypothesis at the 5% significance level with a p-value of 0.9898. This p-value is greater than 0.05 which suggests that there isn't sufficient evidence to conclude that the 'Before' measurements are significantly greater than the 'After' measurements. Therefore, we can conclude that the observed difference is not statistically significant. The 95% confidence interval I obtained is (-15.898, -1.537). PART B: One-Way ANOVA B1:

B2: The value of the total SS I calculated is: 15.2161 + 6.2731 = 21.49 B3: The p-value for the F test statistic allows us to reject the null hypothesis at the 5% level of confidence. We can reject it because the value I got is 9.848996e-10, which is a much smaller value than the 5% level of confidence. B4: Some conclusions I can make based on this analysis are that the Jersey breed tends to have the highest butterfat percentage, while Holstein-Friesian breed appears to have the lowest. Based on Tukey’s HSD test, we can identify which breed means differ significantly and which do not by looking at the p-values. If they are less than 0.05, it indicates significant differences between breeds in their means. The underscore diagram helps visualize the relative differences between the breed means, helping us better understand the variations in Butterfat Percentage across the different breeds.

B5: If Tukey's HSD procedure had used a 10% familywise error rate instead of a 5% level, it would have impacted the determination of statistical significance in the differences between the breed means. Increasing the familywise error rate would lead to a more open and broader set of differences between the breeds. This could alter and expand the conclusions drawn regarding which breed means differ significantly from each other. B6: B7: One possible violation is that there is a slight variation in the appearance of the width of the boxes, also known as the interquartile ranges, which raises the possibility that the homogeneity of variance assumption has been violated. Another possible violation could be shown through the boxplots. Asymmetric boxplot forms in certain breeds suggest that their butterfat percentage distributions may be more skewed. This can suggest a slightly more serious violation of the ANOVA's normality assumption. B8:

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