Studies are finding that bacteria in the stomach are essential for healthy functioning of the human body. One study68 compared the number of unique bacterial genes in stomachs of healthy patients and those of patients with irritable bowel syndrome (IBS). For healthy patients, we have x = 564 million with s = 122 million and n = 99. For those with IBS, we have x̅ = 425 million with s = 127 million and n = 25. Both distributions appear to be approximately normally distributed. Test to see if people with IBS have, on average, significantly fewer unique bacterial genes in their stomachs. Show all details, including giving the degrees of freedom used.