Answer:
a) H0 : P = 0.07
Ha : P ≠ 0.07
b) p -value = 0.1770
Step-by-step explanation:
P = 7% = 0.07
x (result ) = 7 , n = 163
p = x / n = 7 / 163 = 0.043
<u>a) Using a significance level ( ∝ ) of 0.05, estimate the appropriate hypothesis</u>
H0 : P = 0.07
Ha : P ≠ 0.07
conduct a Z- test statistic
Z = ( p - P ) /
= ( 0.043 - 0.07 ) / = - 1.35
Critical value ( Z₀.₀₂₅ ) = ± 1.96
<em>we fail to reject H0 given that | z | < Zcritical because there is not enough evidence to conclude that proportion change</em>
<u>b) Determine the p-value of the test </u>
P-value = P ( | Z | > Z )
= 2 * P ( Z < -1.35 )
= 0.1770
The p-value ( 0.1770 ) > ∝ ( 0.05 ) hence we fail to reject H0 ( i.e. the conclusion agrees with part a above )