Respuesta :
Answer:
The proportion of vehicles on South Cedar Nile that exceeds the speed limit is more than 0.50.
Step-by-step explanation:
A single proportion z test can be applied to test whether more than half of the vehicles on South Cedar Nile exceed the speed limit.
The hypothesis can be defined as:
H₀: The proportion of vehicles on South Cedar Nile that exceeds the speed limit is 0.50, i.e. p = 0.50.
Hₐ: The proportion of vehicles on South Cedar Nile that exceeds the speed limit is more than 0.50, i.e. p > 0.50.
The information provided is:
X = number of vehicles that exceeds the speed limit = 49
n = 73
Compute the sample proportion value as follows:
[tex]\hat p=\frac{X}{n}=\frac{49}{73}=0.671[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.671-0.50}{\sqrt{\frac{0.50(1-0.50)}{73}}}=2.90[/tex]
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
The commonly used significance level are:
α = 0.01, 0.05 and 0.10
Compute the p-value of the test as follows:
[tex]p-value=P(Z>2.90)=1-P(Z<2.90)=1-0.9981=0.0019[/tex]
The p-value of the test is very small.
It will be less than any significance level.
So the null hypothesis will be rejected.
Conclusion:
As the null hypothesis is rejected it can be concluded that the proportion of vehicles on South Cedar Nile that exceeds the speed limit is more than 0.50.
