A random sample of 50 observations of a random variable X and a random sample of 60 observations of a random variable Y are taken. The results for the sample means, x̅ and y̅, and the unbiased estimates for the population variances, S²_x and S²_y, respectively, are as follows.

x̅ = 25.4       y̅ = 23.6      S²_x = 23.2     S²_y = 27.8

A test at the α% significance level, of the null hypothesis that the population means of X and Y are equal, against the alternative hypothesis that they are not equal, is carried out. Given that the null hypothesis is not rejected, find the set of possible values of α.