Question

10-12. A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 2 pounds within a month.” Six clients of this program are weighed on the first day of the diet and then one month later. Let the difference be defined as Weight on First Day of Diet minus Weight One Month Later. (You may find it useful to reference the appropriate table: z table or t table)

Client	Weight on First Day of Diet	Weight One Month Later
1	170	174
2	199	201
3	168	163
4	197	177
5	153	151
6	127	134

Let the difference be defined as Before – After.

a. Specify the null and alternative hypotheses that test the diet center’s claim.

• H₀: μ_D = 2; H_A: μ_D ≠ 2

• H₀: μ_D ≥ 2; H_A: μ_D < 2

• H₀: μ_D ≤ 2; H_A: μ_D > 2

b. Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c. Find the p-value.

• p-value < 0.01

• 0.05  p-value < 0.10
• p-value  0.10
• 0.025  p-value < 0.05
• 0.01  p-value < 0.025

d. At the 5% significance level, do the data support the diet center’s claim?

• No  since the p-value is less than α.
• Yes  since the p-value is more than α.
• Yes  since the p-value is less than α.
• No  since the p-value is more than α.

Answer 1

using excel>addin>phstat>two sample test

we have

Paired t Test
Data
Hypothesized Mean Difference	2
Level of significance	0.05
Intermediate Calculations
Sample Size	6
DBar	2.3333
Degrees of Freedom	5
SD	9.6471
Standard Error	3.9384
t Test Statistic	0.0846
Upper-Tail Test
Upper Critical Value	2.0150
p-Value	0.4679
Do not reject the null hypothesis

a. Specify the null and alternative hypotheses that test the diet center’s claim.

• H₀: μ_D ≤ 2; H_A: μ_D > 2

b. Assuming that weight loss is normally distributed, calculate the value of the test statistic.

t = 0.09

c. Find the p-value.

p-value>0.10

d. At the 5% significance level, do the data support the diet center’s claim?

• No  since the p-value is more than α.