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.
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?