Question

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 5 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	158	151
2	205	200
3	170	169
4	189	179
5	149	144
6	135	129

 

  Click here for the Excel Data File

Let the difference be defined as Before − After.
 

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

multiple choice 1

• H₀: μ_D = 5; H_A: μ_D ≠ 5

• H₀: μ_D ≥ 5; H_A: μ_D < 5

• H₀: μ_D ≤ 5; H_A: μ_D > 5

 

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.

multiple choice 2

• p-value ≤ 0.01

• 0.01 < p-value ≤ 0.025

• 0.025 < p-value ≤ 0.05

• 0.05 < p-value ≤ 0.10

• p-value > 0.10

 

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

multiple choice 3

• Yes, since the p-value is less than or equal to α.

• Yes, since the p-value is greater than α.

• No, since the p-value is less than or equal to α.

• No, since the p-value is greater than α.

• 
  

Answer 1

The statistical software output for this problem is:

From above output:

a) Option C

b) Test statistic = 1.91

c) 0.05 < p - value < 0.10

d) Yes