Answer
a. $σ_p̂$=$\sqrt \frac{0.42*0.58}{400}$=0.025
z= $\frac{0.42-0.45}{0.025}$ =-1.22
α = 0.025,From the table, critical value =1.96
Rejection region = z < -1.96
Non rejection region = z > -1.96
The value z = -1.22 falls within the non-rejection region, hence we failed to reject the null hypothesis.
b. $σ_p̂$=$\sqrt \frac{0.39*0.61}{400}$=0.0244
z= $\frac{0.39-0.45}{0.0244}$ =-2.46
α = 0.025, From the table, critical value = 1.96
Rejection region = z < -1.96
Non rejection region = z > -1.96
The value z = -2.46 falls at the rejection region, hence we reject the null hypothesis.
Work Step by Step
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