Question

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 309 children treated with the​ herb, the mean number of days with fever was 0.91​, with a standard deviation of 1.54 days. Among 370 children given a​ placebo, the mean number of days with fever was 0.73 with a standard deviation of 1.24 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.

Answer 1

The Null Hypothesis and the Alternate Hypothesis is given by:

, i.e, there is no effect of the herbs on the number of days with fever among the children, against

, i.e, there is significant effect of the herbs on the number of days with fever among the children.

Thus, the Student’s t-statistic is given by:

where,

Now, the p-value is obtained as:

Thus, on the basis of p-value we reject the null hypothesis if and only if,

Here, we observe that, , and hence do not reject the null hypothesis at level of significance and thus conclude that there might be no effect of the herbs on the number of days with fever among the children.