Question

In a pilot study for testing the "truth" to the theory that, on average, U.S. adults gain weight between Thanksgiving and January, a research team looked at responses from 8 randomly selected U.S. adults. The subjects were weighed (lb) on the day before Thanksgiving and again on January 3^rd The raw data are found in Table 1. Let α = 0.05

Table 1: Weights (lb) before Thanksgiving and on Jan. 3^rd for 8 U.S. adults

Pre-Thanksgiving	146.1	157.7	150.7	152.5	154.8	153.3	151.2	148.1
Jan. 3rd	156.5	157.0	156.1	158.2	151.9	156.5	155.4	153.5
Diff
Since the researchers believe that adults, on average, gain weight you should compute the differences as Jan. 3 - PreThanksgiving and expect positive numbers.

a. Fill in the missing table cells for the weight differences per the directions outlined in the bottom caption.

b. The researchers want to know if the data provide strong evidence that, on average, U.S. adults gain weight between Thanksgiving and January.
The appropriate null/alternative hypothesis pair for this study is:
(you have two attempts at this question)

H₀: μ_d = 0 ; H_A: μ_d > 0H₀: μ_d = 0 ; H_A: μ_d < 0     H₀: μ_d = 0 ; H_A: μ_d ≠ 0H₀: μ₁ - μ₂ = 0 ; H_A: μ₁ - μ₂ ≠ 0H₀: μ₁ - μ₂ = 0 ; H_A: μ₁ - μ₂ < 0H₀: μ₁ - μ₂ = 0 ; H_A: μ₁ - μ₂ > 0

c. The test statistic for this data set is:  
     Note: Round your answer to the nearest hundredth.


d. The p-value for this study is:  
Note: round your answer to 4 decimal precision.
Also recall from the first problem that, when testing the value of a single mean, df = n - 1.

e. Based on this we:
(you have two attempts at this question)

FTR H₀ because the p-value is greater than the significance levelReject H₀ because the p-value is greater than the significance level    Reject H_A because the p-value is less than to the significance levelReject H₀ because the p-value is less than the significance levelFTR H_A because the p-value is less than to the significance levelFTR H₀ because the p-value is less than the significance level

Answer 1