Question

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. 10) The table below shows the weights of seven subjects before and after following a particular diet for two months.

Subject A B C D E F G

Before 182 178 199 194 151 188 170

After 175 169 197 199 137 190 158

Using a 0.01 level of significance, test the claim that the diet is effective in reducing weight.

Answer 1

Before	After	Difference(d)
182	175	7
178	169	9
199	197	2
194	199	-5
151	137	14
188	190	-2
170	158	12
	Total	37

Claim: The diet is effective in reducing weight.

The null and alternative hypothesis is

Level of significance = 0.01

Sample size = n = 7

Sample mean of difference = = 5.2857

Sample standard deviation of difference = = 7.1581

Test statistic is

Degrees of freedom = n - 1 = 7 - 1 = 6

Critical value = 3.143   ( Using t table)

Test statistic < critical value we fail to reject null hypothesis.

Conclusion:

The diet is NOT effective in reducing weight.