Answer:
a)
<em>The statistic value |Z| = 2.053 > 1.96 at 0.05 Level of significance</em>
<em>Null hypothesis is rejected</em>
<em>Alternative hypothesis is Accepted</em>
<em> Actually 30% of all drivers make not this mistake at the given intersection</em>
<em>b)</em>
<em>The test statistic value |Z| = 2.053 >2.576 at 0.01 Level of significance</em>
<em>Null hypothesis is Accepted</em>
<em> Actually 30% of all drivers make this mistake at the given intersection</em>
Step-by-step explanation:
<u><em>Step(i):</em></u>-
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
<em>Null hypothesis:- H₀: p = 0.30</em>
<em>Alternative hypothesis : H₁:p≠0.30</em>
<u><em>Step(ii):-</em></u>
a)
<em>Test statistic </em>
Z = -2.053
<em> |Z| = |-2.053| = 2.053</em>
<em>Level of significance = 0.05</em>
<em>Z₀.₀₅ = 1.96</em>
<em>The calculated value |Z| = 2.053 > 1.96 at 0.05 Level of significance</em>
<em>Null hypothesis is rejected</em>
<em>Alternative hypothesis is Accepted</em>
<u><em>Conclusion:</em></u><em>-</em>
<em> Actually 30% of all drivers make not this mistake at the given intersection</em>
<em>b)</em>
<em>Given level of significance = 0.01</em>
<em>Z₀.₀₁ = 2.576</em>
<em>The calculated value |Z| = 2.053 >2.576 at 0.01 Level of significance</em>
<em>Null hypothesis is Accepted</em>
<em> Actually 30% of all drivers make this mistake at the given intersection</em>