Answer :
Answer:
The difference value are: {2, 0, 1, 2, 0}.
Step-by-step explanation:
In this case we have to perform a paired t-test.
The hypothesis is:
H₀: [tex]\mu_{d}\leq 0[/tex] vs. Hₐ: [tex]\mu_{d}>0[/tex]
The test statistic is:
[tex]t=\frac{\bar d-\mu_{d}}{SE_{d}}[/tex]
The formula to compute the value of [tex]\bar d[/tex] is:
[tex]\bar d=\frac{\sum d}{n}[/tex]
The formula to compute the standard error of d is:
[tex]SE_{d} =\frac{SD_{d}}{\sqrt{n}}\\SD_{d}=\frac{\sum (d-\bar d)^{2}}{n-1}[/tex]
The difference value for each element is computed is computed using the formula:
[tex]d=Populaion\ 1-Population\ 2[/tex]
The differences are:
d₁ = 21 - 19 = 2
d₂ = 28 - 28 = 0
d₃ = 18 -17 = 1
d₄ = 20 -18 = 2
d₅ = 26 -26 = 0
Thus, the difference value are: {2, 0, 1, 2, 0}.