Respuesta :
Answer:
a)
The statistic value |Z| = 2.053 > 1.96 at 0.05 Level of significance
Null hypothesis is rejected
Alternative hypothesis is Accepted
Actually 30% of all drivers make not this mistake at the given intersection
b)
The test statistic value |Z| = 2.053 >2.576 at 0.01 Level of significance
Null hypothesis is Accepted
Actually 30% of all drivers make this mistake at the given intersection
Step-by-step explanation:
Step(i):-
Given Population proportion = 30% or 0.30
Given data In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{157}{600} = 0.2616[/tex]
Null hypothesis:- H₀: p = 0.30
Alternative hypothesis : H₁:p≠0.30
Step(ii):-
a)
Test statistic
[tex]Z = \frac{p^{-}-P }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
[tex]Z = \frac{0.2616-0.30 }{\sqrt{\frac{0.30(1-0.30)}{600} } }[/tex]
Z = -2.053
|Z| = |-2.053| = 2.053
Level of significance = 0.05
Z₀.₀₅ = 1.96
The calculated value |Z| = 2.053 > 1.96 at 0.05 Level of significance
Null hypothesis is rejected
Alternative hypothesis is Accepted
Conclusion:-
Actually 30% of all drivers make not this mistake at the given intersection
b)
Given level of significance = 0.01
Z₀.₀₁ = 2.576
The calculated value |Z| = 2.053 >2.576 at 0.01 Level of significance
Null hypothesis is Accepted
Actually 30% of all drivers make this mistake at the given intersection
