In: Statistics and Probability
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.
Null hypothesis : Ho : Average weight loss 3;
Ho :
Alternate hypothesis : Ha : Average weight loss > 3
Ha : (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 : Ho : Average weight loss 5;
Ho :
Alternate hypothesis : Ha : Average weight loss > 3
Ha : (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