Question

A dietary supplement is promising weight loss in 2 weeks using their product. A sample of 10 people were weighed before starting the supplement and 2 weeks after using the supplement. Using a 5% significance level, is there statistically sufficient evidence to support the claim that there was weight loss after taking the supplement for 2 weeks? Perform an appropriate hypothesis test showing necessary statistical evidence to support your conclusion.

Before	After
175	174
186	184
187	187
185	184
171	167
166	168
180	180
164	162
174	175
165	164

CONCLUSION:

Answer 1

The table given below ,

Before(X)	After(Y)	d-=X-Y	di^2
175	174	1	1
186	184	2	4
187	187	0	0
185	184	1	1
171	167	4	16
166	168	-2	4
180	180	0	0
164	162	2	4
174	175	-1	1
165	164	1	1
	Total	8	32

From table ,

Let ,

1) Hypothesis : VS  

2) The test statistic is ,

3) Critical value : ; from t-table

4) Decision : Here ,

Therefore , fail to reject the null hypothesis.

5) Conclusion : Hence , there is not sufficient evidence to support the claim that there was weight loss after taking the supplement for 2 weeks.