Three tests are proposed based on F-distribution, Likelihood Ratio Test (LRT) and large sample Z-test for intraclass correlation coefficient under unequal family sizes based on a single multinormal sample. It has been found that the test based on F-distribution consistently and reliably produces results superior to those of Likelihood Ratio Test (LRT) and large sample Z-test in terms of size for various combinations of intraclass correlation coefficient values. The power of this test based on F-distribution is competitive with the power of the LRT and the power of Z-test is slightly better than the powers of F-test and LRT when k = 15, but the power of Z-test is worse in comparison with the F-test and LRT for k = 30, i.e. for large sample situation, where k = sample size. This test based on F-distribution can be used for both small sample and large sample situations. An example with real data is presented.