If the null hypothesis is true, but we reject it, we have made a Type I error. This is also known as a "false positive" result.

When you reject the null hypothesis in a Mann-Whitney U test, you conclude that there is a difference between the groups. More specifically, it means that it is unlikely that a randomly selected value from the first group is greater than a randomly selected value from the second group with a probability of 0.5.

The assumptions of a multiple linear regression model can be validated by checking the residuals plot for randomness (i.e., no patterns), conducting a normality test on the residuals to check if they are normally distributed, and checking for homoscedasticity (i.e., constant variance of the residuals).

If all the values in a dataset are identical, there is no variation or dispersion in the data. Hence, both the variance and the standard deviation would be zero.

The harmonic mean is a measure of central tendency that is much less well known than, for example, the arithmetic mean or the median. It is appropriate for situations when the average of rates is desired. The harmonic mean is calculated by taking the reciprocal of the arithmetic mean of the reciprocals.

While applying ANOVA, the following assumptions are made: Normality (data is normally distributed), Homogeneity of variance (variance among the groups is approximately equal), Independence (the observations are independent of each other).

Interval estimation in inferential statistics is a method by which a range of values is provided that is likely to contain the population parameter. Instead of a single value, it provides an interval of estimates making it more flexible and informative than point estimation.

Non-parametric tests treat data points by analyzing their ranks rather than their actual values. This makes non-parametric tests less sensitive to extreme values and makes them a good choice when dealing with skewed data or data with many outliers.

The Central Limit Theorem is a fundamental theorem in statistics that states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, no matter what the shape of the population distribution. This outcome is significant because it enables us to make statistical inferences about the population mean based on the distribution of sample means.

Checking the assumptions of a multiple linear regression model (like linearity, independence, normality, and homoscedasticity) is crucial to ensure the validity of the model and its estimates. Violations of these assumptions can lead to biased or inefficient estimates, and inferences made from such models could be misleading.