Choose the correct code for the following statements being correct or incorrect
Statement I: The geometric mean of the two regression coefficients of X and Y variables gives the value of the coefficient of correlation.
Statement II: If the population distribution is not normal and a sampling distribution of mean is prepared by taking small sized samples, the sampling distribution of mean is not normal.
- Both the statements I and II are correct
Both the statements I and II are incorrect
Statement I is correct, but II is incorrect
Statement II is correct, but I is incorrect.
Answer (Detailed Solution Below)
Option 1 : Both the statements I and II are correct
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Statement I: The geometric mean of the two regression coefficients of X and Y variables gives the value of the coefficient of correlation.
Explanation:
- The regression coefficient is a statistical measure of the average functional relationship between two or more variables.
- In regression analysis, one variable is considered as dependent and the other(s) as an independent.
- Thus, it measures the degree of dependence of one variable on the other(s).
- The geometric mean between the two regression coefficients is equal to the coefficient of correlation, r = .
Thus, the statement I is correct.
Statement II: If the population distribution is not normal and the sampling distribution of mean is prepared by taking small-sized samples, the sampling distribution of mean is not normal.
Explanation:
- The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger.
- Thus, if the sampling distribution of mean is prepared by taking small-sized samples, the distribution will not be normal.
Thus, statement II is also correct.
Therefore, option I is the correct answer.