# 5% significance difference

I need help with this question please. To test the effectiveness of a diet 10 patients are placed on a diet for one month. They are weighted before and after the study. Their initial weight is 198,237,233,179,219,169,222,167,199,233 and their final weight is 192,225,226,172,214,161,210,161,193,226. Using a 5% level of significance is there a significant difference between the set of measurements due to the diet.

• Is this a homework related question? If so, please add the tag self-study to your question and read this information. – javlacalle Oct 12 '14 at 19:47

## 1 Answer

If you can assume that the observations are drawn from a Normal distribution, you can perform a paired t-test. Since there is a treatment, it's probably best to assume that that the pre-treatment and post-treatment variance will be different. In R,

> weight_before = c(198,237,233,179,219,169,222,167,199,233)
> weight_after = c(192,225,226,172,214,161,210,161,193,226)
> test_results = t.test(weight_before, weight_after, paired=TRUE, var.equal=FALSE)
> test_results$p.value  4.321527e-06  This p-value is less than your$0.05\$ significance level. So what does this mean under the null hypothesis of the t-test?