In situations where the experimental or sampling units in a study can be easily ranked than quantified, Mcintyre (1952) proposed the notion of a ranked set sample ( RSS), and observed that, to estimate the population mean, the sample mean based on a RSS sample of size n provides an unbiased estimator with a smaller variance compared to a simple random sample mean of the same size n. Mcintyre's concept of RSS is essentially nonparametric in nature in that the underlying population distribution is assumed to be completely unknown. Sinha et al. (1992) in a recent paper further explored the concept of RSS and its many variations for estimation of a normal mean and a normal variance, and an exponential mean. In this paper we use the concept of RSS to derive tests for a normal mean μ when the variance is known, and show that many improved tests can be constructed, all of which are much better than the traditional normal test. All our tests are based on the improved eetimators of μ derived in Sinha et. al. (1992).