Answer
a. $σ_p̂$=$\sqrt \frac{0.86*0.14}{600}$=0.0142
z= $\frac{0.86-0.82}{0.0142}$ =2.82
α = .02/2=0.01, critical value = 2.326
Rejection region = z< -2.326 or z >2.326
Non rejection region =-2.326 < z < 2.326
The value z = 2.82 falls at the rejection region, hence we reject the null hypothesis.
b. The probability of making a Type I error : α = 0.02
c. By p value approach,
If α = 0.025,
p-value = P(Z>2.82) = 0.0024 < α
The p-value =0.0024 is smaller than α , hence we reject the null hypothesis.
If α = 0.01,
p-value = P(Z>2.82) = 0.0024 < α
The p-value =0.0024 is smaller than α , hence we reject the null hypothesis.
Work Step by Step
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