Researchers estimating a wage equation with a sample of adult males suspect a structural break between wages and age around age 55. To investigate this issue, they estimate the following model and test
Ho: β_2=β_3=0
log⁡(wage)=βo+β_1 age+β_2 old+β

The usual F-test of Ho would be adversely affected if there are differences in the variability of wages for those less than 55 compared to those greater than 55 because the test assumes that the variance of the residuals is constant across all observation in the sample. If the variance of the residuals is not the same for observations in the sample, then the test is no longer valid. If there is a structural break around age 55, then it is likely that the variance of the residuals is different for those less than 55 compared to those greater than 55 and the test results may not provide an accurate estimation of the coefficients of the model.