The article "Evaluation of Criteria for Setting Speed Limits on Gravel Roads" (S. Dissanayake, Journal of Transportation Engineering, 2011:57-63) measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed, and 49 of them were exceeding the speed limit. Can you conclude that more than half of the vehicles on South Cedar Niles exceed the speed limit?

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:

The test statistic is:

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:

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.

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