Abstract: The null distribution of the likelihood ratio test (LRT) of a onecomponent normal model versus two-component normal mixture model is

unknown. In this paper, we take a bootstrap approach to the likelihood ratio

test for testing bimodality of plasma glucose concentrations from Rancho

Bernardo Diabetes Study. The small p-values from this approach support the

hypothesis that a bimodal normal mixture model fits the data significantly

better than a unimodal normal model. The size and power of the bootstrap

based LRT are evaluated through simulations. The results suggest that a

sample size of close to 500 would be necessary in order to attain a power of

90% for detecting the unbalanced mixtures with means and variances similar

to those in the Rancho Bernardo data. Besides sample size, the power also

depends on the two means and variances of the two components in the data.