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...

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 333 children treated with the​ herb, the mean number of days with fever was 0.89​, with a standard deviation of 1.51 days. Among 379 children given a​ placebo, the mean number of days with fever was 0.68 with a standard deviation of 1.06 days. Use a 0.01 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.