Question

1. A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least 3 pounds. Eight subjects use the product for one month, and the resulting weight loss data are reported below. Use hypothesis-testing procedures to answer the following questions

Subject	Initial Weight (lb)	Final Weight (lb)
1	165	161
2	201	195
3	195	192
4	198	193
5	155	150
6	143	141
7	150	146
8	187	183

a.) Do the data support the claim of the producer of the dietary product with 0.05? Show all the steps in hypothesis testing.

b.) Do the data support the claim of the producer of the dietary product with 0.01? Explain.

c.) In an effort to improve sales, the producer is considering changing its claim from “at least 3 pounds” to “at least 5 pounds.” Repeat parts (a) and (b) to test this new claim.

Answer 1

Null hypothesis : H_o : Average weight loss 3;

H_o :  

Alternate hypothesis : H_a : Average weight loss > 3

H_a : (Right Tailed test)

x : Initial weight

y : Final weight

d : x-y

Sample mean weight loss

Sample standard deviation of weight loss :

Subject	Initial Weight (lb)	Final Weight (lb)	d	(d-d)	(d-d)2
1	165	161	4	-0.125	0.015625
2	201	195	6	1.875	3.515625
3	195	192	3	-1.125	1.265625
4	198	193	5	0.875	0.765625
5	155	150	5	0.875	0.765625
6	143	141	2	-2.125	4.515625
7	150	146	4	-0.125	0.015625
8	187	183	4	-0.125	0.015625
		Total	33		10.875
		Mean = 33/8	4.125

Degrees of freedom = n-1 = 8-1 =7

For right tailed test ;

a.) Do the data support the claim of the producer of the dietary product with 0.05

As P-Value i.e. is less than Level of significance i.e (P-value:0.019 < 0.05:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the Average weight loss > 3. Therefore the data do support the claim of the producer of the dietary product with 0.05

b.) Do the data support the claim of the producer of the dietary product with 0.01

As P-Value i.e. is greater than Level of significance i.e (P-value:0.019 > 0.01:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that average weight loss is > 3. Therefore the data do not support the claim of the producer of the dietary product with 0.01

c)

In an effort to improve sales, the producer is considering changing its claim from “at least 3 pounds” to “at least 5 pounds.

Null hypothesis : H_o : Average weight loss 5;

H_o :  

Alternate hypothesis : H_a : Average weight loss > 3

H_a : (Right Tailed test)

For right tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.9563 > 0.05:Level of significance); Fail to Reject Null Hypothesis
There is not sufficient evidence to conclude that average weight loss is > 5. Therefore the data do not support the claim of the producer of the dietary product with 0.05

As P-Value i.e. is greater than Level of significance i.e (P-value:0.9563 > 0.01:Level of significance); Fail to Reject Null Hypothesis

There is not sufficient evidence to conclude that average weight loss is > 5. Therefore the data do not support the claim of the producer of the dietary product with 0.01