Question

2. A liquid dietary product claim that the use of the product for one month results in an average weight loss of at least 3 lbs. Eight people weight data is given use the product and resulting follows as Initial Weight Final Weight 165 161 201 195 195 192 198 193 155 150 143 141 150 146 187 183 a) Does this data set support the claim from the producer? (use a 0.05) b) One sales manager actually claims that this product will reduce average weight by at least 5 pounds, does the data support this claim?

Answer 1

ANSWER:

a)

Table of comparison:

Initial wt	Final wt	Reduction
165	161	4
201	195	6
195	192	3
198	193	5
155	150	5
143	141	2
150	146	4
187	183	4

Xbar = 4.125 and sigma = 1.2464

z = xbar -mu /sigma_xbar = 4.125 - 3 / 1.24 / (8)^1/2 = 1.125 / 0.43 = 2.56

z value corresponding to aplha = 0.05 is 1.96

Since the calculated value of z falls in the rejection region, the claim is false.

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(b)

for mu =5

z = 4.125-5 / 0.43 = -2.03

Which is also beyond the value -1.96 so the claim is rejected.