Answer:
(a) The correct interval is, 0.010 < p-value < 0.025. Fail to reject H₀.
(b) The correct interval is, p-value > 0.100. Fail to reject H₀.
Step-by-step explanation:
(a)
The information provided is:
Hₐ: μ > 0.5, n = 21, t = 2.485
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}>2.485)[/tex]
[tex]=P(T_{20}>2.485)\\=\text{T.DIST.RT(2.485,20)}\\=0.011[/tex]
The correct interval is, 0.010 < p-value < 0.025.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
p-value = 0.011 > α = 0.01
Fail to reject H₀.
(b)
The information provided is:
Hₐ: μ < 3, n = 17, t = 0.5
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}>0.5)[/tex]
[tex]=P(t_{16}>0.5)\\=\text{T.DIST.RT(0.5,16)}\\=0.312[/tex]
The correct interval is, p-value > 0.100.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
p-value = 0.312 > α = 0.01
Fail to reject H₀.