The main terms of interval data analysis was initially founded the measurement theory in metrology where an interval uncertainty is naturally introduced. It is expected that every observation is measured by an instrument with absolute error Delta. Thus, if the precise value of an observed response is <(x)over dot>, measurement error is e is an element of[-Delta,Delta], then the measurement is equal to x = <(x)over dot>+e. In this case, we deal with a usual complete sample X-n = {X-1,..., X-n}. Nevertheless, the measurement can be represented as an interval (x-Delta, x+Delta) = (L, R). In this case, for the sample of n observations we obtain an interval sample of the form I-n = {(L-1, R-1),..., (L-n, R-n)}. The main idea of nonparametric estimation of the distribution function with interval data is based on maximization of the loglikelihood function In L(I-n) = Sigma(n)(i=1) ln (F(R-i)-(F(L-i)) at the boundary points of observations L-i, R-i, i = (1,n) over bar under condition of monotonicity of the distribution function. The Turnbull and ICM algorithms are used for calculation of the nonparametric estimate of the distribution function with interval data. The accuracy of the estimates calculation is the same for both algorithm, but the computing time is less for the ICM algorithm. Unknown distribution parameters can be estimated by the maximum likelihood method, which is based on the maximization of likelihood function by parameter theta: L(I-n vertical bar theta) = Pi(n)(i=1) (F(R-i vertical bar theta) - F(L-i vertical bar theta)). Thus, the maximum likelihood estimates can be written as (theta) over cap = argmax ln L(I-n|theta)(theta)is an element of Theta(theta=Theta.) In this paper, the modifications of the classical goodness-of-fit tests for composite hypothesis H-0 : F(t) is an element of {F-0(t;theta),theta is an element of Theta} have been proposed. The main idea of this modification is based on the usage of nonparametric estimate of the distribution function, obtained by the ICM algorithm, instead of the empirical distribution function. In this case, we have the test statistic of the Kolmogorov type as D-n = sup(0 < t <tau m)vertical bar(F) over cap (t) - F-0(t,(theta) over cap vertical bar the statistic of Cramer-von Mises-Smirnov type test as S-omega 2 = integral(tau m)(0)((F) over cap (n)(t) - F-0(t,(theta) over cap))(2) dF(0)(t,(theta) over cap), and the statistic of Anderson-Darling type test as S-W = integral(tau m)(0)((F) over cap (n)(t) - F-0(t,(theta) over cap))(2) dF(0)(t,(theta) over cap)/F-0(t,(theta) over cap)(1-F-0(t,(theta) over cap)), where (F) over capn(t) is the nonparametric estimate of the distribution function by the interval data, 0 < tau(0) < tau(1) <... <tau(m) are ordered different values L-i and R-i, i=(1,n) over bar. We have formulated the sequence of steps for estimation of the p-value for the proposed tests. The hypothesis is not rejected if the obtained p-value is larger than the significance level alpha. As an example, we have tested the normality hypothesis by the interval sample of consumer demand prices for bioenergy drink SPC "SAVA". It has been shown that there is no reason for rejecting the hypothesis of normality of consumer demand prices.
