An oceanographer wants to check whether the average depth of the ocean in a certain region is 55 fathoms, as had been previously reported. He took soundings at 36 randomly chosen locations in the region and obtained a sample mean of 56.4 fathoms with a sample standard deviation of 5.1 fathoms. Are these data significant enough to reject the null hypothesis that the mean depth is 55 fathoms, at the
(a) 10 percent
(b) 5 percent
(c) 1 percent
level of significance?