Question

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.

Subject Initial Weight (in lbs) Final Weight (in lbs)
1 165 161
2    201   195
3 195 192
4 198 193
5 155 150
6     143 141
7 150 146
8 187 183
1.What is the appropriate alternative hypothesis for this problem?

a. μ1 - μ2 ≥ 3

b. μD ≤ 3

c. μ1 - μ2 > 3

d. μD < 3

2. Based on the appropriate hypothesis statements for this problem, do you have a one-tailed test or a two-tailed test?

a. One-tailed test

b. Cannot be determined

c. Can be either one-tailed or two-tailed

d. Two-tailed test

3. What is the appropriate test statistic to be used for this problem?

a. chi-square

b. t

c. f

d. z

4. What is the value of the computed test statistic?

a. 0.191

b. 0.097

c. 0.196

d. 2.553

5. Do the data support the claim of the producer of the dietary product with the probability of type I error set to 0.05?

a. Yes, data supports producer's claim.

b. It really depends on the metabolism of the person.

c. Cannot be determined.

d. No, data does not support producer's claim.

Answer 1

= (4 + 6 + 3 + 5 + 5 + 2 + 4 + 4)/8 = 4.125

s_d = sqrt(((4 - 4.125)^2 + (6 - 4.125)^2 + (3 - 4.125)^2 + (5 - 4.125)^2 + (5 - 4.125)^2 + (2 - 4.125)^2 + (4 - 4.125)^2 + (4 - 4.125)^2)/7) = 1.2464

1) Option - D)

Option - a) One-tailed test

Option - b) t

The test statistic is

  

  

df = 8 - 1 = 7

At alha = 0.05, the critical value is -t_{0.05, 7} = -1.895

Since the test statistic value is not less than the critical value (2.553 > -1.895), so we should not reject the null hypothesis.

Option - a) Yes, data supports producer's claim.