- From the above plots, we can say that the distribution of diabetes from obesity_diabetes datasets is approximately normal with a small peak at the right side of the mean, whereas the distribution of diabetes from the inactivity_diabetes dataset is a little right-skewed.
- By assuming that the basic assumptions of the t-test are true, I have performed the hypothesis testing as follows:
The assumptions of the t-test are:
- The observations within each group must be independent of each other.
- The data within each group should follow a normal distribution.
- The variances of the two groups should be approximately equal.
- The samples from the two groups should be randomly selected from the respective populations.
Hypothesis Testing:
- H0 (Null Hypothesis): There is no significant difference in the means of the two datasets.
- H1 (Alternative Hypothesis): There is a significant difference in the means of the two datasets.
Monte Carlo Simulation:
- The observed t-statistic of approximately -8.587 is a measure of how different the means of your two datasets are. The negative sign indicates that the mean of the first group (group1) is significantly lower than the mean of the second group (group2).
- The Monte Carlo estimated p-value of 0.0 represents the probability of obtaining a t-statistic as extreme as or more extreme than the observed t-statistic under the null hypothesis (i.e., no difference in means).
- A p-value of 0.0 indicates that the observed difference in means is highly unlikely to have occurred by random chance alone.
- With the obtained p-value of 0.0, we reject the null hypothesis (H0) and conclude that there is a significant difference in the means of the two datasets. In other words, the difference in means between group1 and group2 is statistically significant, and it is unlikely to be due to random variation.