The State Transportation Department Is Thinking of Changing Its Speed

question 67

Multiple Choice

The State Transportation Department is thinking of changing its speed limit signs. It is considering two new options in addition to the existing sign design. At question is whether the three sign designs will produce the same mean speed. To test this, the department has conducted a limited test in which a stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05, what is the critical value for this hypothesis test?

• A) F = approximately 3.15
• B) F = approximately 4.90
• C) F = approximately 29.47
• D) F = approximately 2.70

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Definitions:

Type II Error

A statistical error that occurs when a false null hypothesis is not rejected, meaning a real effect or difference was failed to be detected.

Sample Size

The number of observations or data points collected in a sample from a population, used for statistical analysis.

Power of Test

Refers to the probability that the test correctly rejects the null hypothesis when the alternative hypothesis is true.

Type II Error

The error made when a statistical test fails to reject a false null hypothesis, also known as a false negative outcome.