The correct answer is: C. Statement I is true, while Statement II is false.
Statement I is true. If the alternative hypothesis is as $\mu \ne {\mu _0}$, then the researcher requires a two-tailed test. This is because a two-tailed test is used to test for a difference in means that is not equal to zero.
Statement II is false. The mean of the sampling distribution of mean is equal to the parametric value of mean, if the population is normally distributed.
Here is a more detailed explanation of each statement:
Statement I: If the alternative hypothesis is as $\mu \ne {\mu _0}$ ; a researcher requires two-tailed test in hypothesis-testing.
The alternative hypothesis is the statement that the researcher is trying to prove. In this case, the alternative hypothesis is that the mean is not equal to the hypothesized value, $\mu_0$. If the alternative hypothesis is $\mu \ne {\mu _0}$, then the researcher requires a two-tailed test. This is because a two-tailed test is used to test for a difference in means that is not equal to zero.
Statement II: The mean of the sampling distribution of mean is not equal to the parametric value of mean.
The mean of the sampling distribution of mean is the expected value of the sample mean. It is equal to the population mean, $\mu$, if the population is normally distributed.
Therefore, Statement I is true, while Statement II is false.