Answer:
P- value = 0.0069
Step-by-step explanation:
Given that :
sample size n = 1600
The sample proportion [tex]\hat p[/tex] = 0.42
The population proportion p = 0.39
The null hypothesis and the alternative hypothesis can be expressed as:
[tex]H_o : p =0. 39[/tex]
[tex]H_1 : p >0.39[/tex]
The test statistics can be computed as follows:
[tex]Z = \dfrac{\hat p - p }{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]Z = \dfrac{0.42 - 0.39 }{\sqrt{\dfrac{0.39(1-0.39)}{1600}}}[/tex]
[tex]Z = \dfrac{0.03 }{\sqrt{\dfrac{0.2379}{1600}}}[/tex]
[tex]Z = \dfrac{0.03 }{\sqrt{1.486875 \times 10^{-4}}}[/tex]
[tex]Z = \dfrac{0.03 }{0.0121937484}[/tex]
[tex]Z = 2.4603[/tex]
Z [tex]\simeq[/tex] 2.46
Determine the P-value of the test statistic.
The P- value = P(Z > [tex]Z_o[/tex] )
P- value = 1 - P( Z ≤ 2.46)
Using the Excel Function ( = NORMSDIST (2.46))
P- value = 1 - 0.993053
P- value = 0.006947
P- value = 0.0069 to four decimal places
