Answer:
a) -1.25
b) 0.2112
c) -1.96
Step-by-step explanation:
Data provided in the question:
Sample size, n = 400
H0 : p = 20
[tex]\bar{p}[/tex] = 175
Now,
a) The test statistic is given as:
Z = [tex]\frac{(\bar{p}-p)}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
on substituting the respective values, we get
Z = [tex]\frac{(0.175-0.2)}{\sqrt{\frac{0.2\times0.8}{400}}}[/tex]
= -1.25
b) The p-value = 2 × P(Z <-1.25)
Now from the standard normal table
P(Z <-1.25) = 10.56% = 0.1056
Thus,
p-value = 2 × 1056 = 0.2112
c) for a = 0.05,
the critical value is [tex]Z_{\frac{a}{2}}=Z_{\frac{0.05}{2}}[/tex] i.e [tex]Z_{0.025}[/tex]
Now from standard normal table
[tex]Z_{0.025}[/tex] = -1.96
