Question

1. H₀: µ ≥ 205 versus H₁:µ < 205, x= 198, σ= 15, n= 20, α= 0.05

test statistic___________        p-value___________      Decision (circle one)        Reject the H₀       Fail to reject the H₀

2. H₀: µ = 26 versus H₁: µ<> 26,x= 22, s= 10, n= 30, α= 0.01

test statistic___________        p-value___________      Decision (circle one)        Reject the H₀       Fail to reject the H₀

3. H₀: µ ≥ 155 versus H₁:µ < 155, x= 145, σ= 19, n= 25, α= 0.01

test statistic___________        p-value___________      Decision (circle one)        Reject the H₀       Fail to reject the H₀

Answer 1

#1.
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (198 - 205)/(15/sqrt(20))
z = -2.09

P-value Approach
P-value = 0.0183
As P-value < 0.05, reject the null hypothesis.

#2.
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (22 - 26)/(10/sqrt(30))
t = -2.191

P-value Approach
P-value = 0.0366

As P-value >= 0.01, fail to reject null hypothesis.

#3.
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (145 - 155)/(19/sqrt(25))
z = -2.63

P-value Approach
P-value = 0.0043
As P-value < 0.01, reject the null hypothesis.