A new parametric hypothesis test of the mean interval for p-dimensional interval-valued (hyper-rectangles) dataset is proposed under the assumption that the lower bound and the upper bound of an interval are two repeated measurements and the p-dimensional lower bounds and p-dimensional upper bounds have the same variance-covariance matrix. An orthogonal transformation is employed to obtain an equivalent hypothesis test of p-dimensional mean interval of interval-valued dataset in terms of a normal p-dimensional vector of mid-points and a log-normal p-dimensional vector of ranges of the p-dimensional interval-valued dataset. The mean vector of the normal data is tested using Hotelling’s T square, while testing for the mean vector of the log-normal data is performed via the construction of a generalized pivotal quantity in a Monte Carlo simulation. The performance of the proposed test is illustrated with a real-life example.