In a randomized​ double-blind, placebo-controlled trial of​ children, an herb was tested as a treatment for upper respiratory infections in children.​ "Days of​ fever" was one criterion used to measure effects. Among children treated with the​ herb, the mean number of days with fever was ​, with a standard deviation of days. Among children given a​ placebo, the mean number of days with fever was with a standard deviation of days. Use a significance level to test the claim that the herb affects the number of days with fever. Based on these​ results, does the herb appear to be​ effective? Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Let population 1 be children treated with the herb. Find the test statistics.