Answer
a. $σ_p̂$=$\sqrt \frac{0.39*0.61}{450}$=0.0230
z= $\frac{0.39-0.44}{0.0230}$ =-2.17
α = .02, critical value = 2.05
Rejection region = z < -2.05
Non rejection region = z > 2.05
The value z = -2.17 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 = 0.01,
p-value = P(Z>2.17) = 0.015 > α
The p-value =0.0024 is larger than α , hence we failed to reject the null hypothesis.
If α = 0.025,
p-value = P(Z>2.17) = 0.015 < α
The p-value =0.015 is smaller than α , hence we reject the null hypothesis.
Work Step by Step
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