Five people were selected at random for a weight loss diet p

Five people were selected at random for a weight loss diet program. The following ordered pairs are of the form (“Weight Before Diet”, “Weight After Diet”), where weights are measured in kilograms: (80, 72), (93, 89), (98, 93), (102, 104), (100, 97). Let the distributions of weights before the diet correspond to “Population 1.” If we wished to learn if the diet was effective using the Wilcoxon Signed Ranks test, what is the value of T?

Solution

The signed rank is

The value of test statistics is W = sum of signed ranks = 13

For n = 5, at 5% level of significance, the critical value is 15. Since, calculated W is less than critical value, there is no significant difference the weights before and after diet.