To investigate the hypothesis that a horse's chances of winning an eight-horse race on a circular track are affected by its position in the starting lineup, the starting position of each of 144 winners was recorded. It turned out that 29 of these winners had starting position one (closest to the rail on the inside track). We model the number of winners with starting position one by a random variable T with a Bin (144, p) distribution. We test the hypothesis :p-1/8 against :p > 1/ 8 at level -0.01 with T as test statistic.

Does the test procure involve a right or left critical value?

For critical values of T2k, we reject the null hypothesis in favor of the alternative. What is the minimum integer k, using MS-Excel binom.dist?