Question

USE CALCULATOR AND SHOW EVERYSTEP USING CALCULATOR INCLUDING THE NUMBERS USE INPUT IN THE TEST. New road signs are made with the intention of improving visibility for drivers. Highway safety engineers setup a test course that included both the old and new signs. Volunteers drove the course and rated the old and new signs in terms of visibility? (2 points each)

a) Write the null and alternative hypotheses in words using “improved visibility” and “not improved visibility”.

b) Describe a Type I error in the context of the problem.

c) What would be the real-world consequences be if a Type I error occurred?

d) Describe a Type II error in the context of the problem.

e) What would be the real-world consequences be if a Type II error occurred?

Answer 1

(a)

H0:Null Hypothesis: There is no improved visibility due to new signs in place of old signs.

HA:Alternativ Hypothesis: There is improved visibility due to new signs in place of old signs.

(b)

Type I error: Reject a True Null Hypothesis.

Suppose in reality: There is no improved visibility due to new signs in place of old signs. Due to hypothesis testing, Highway Safety Enginners wrongly conclude that : There is improved visibility due to new signs in place of old signs. Type I Error is committed in this situation.

(c) Real world consequence if a Type I error occurred:

Highway Safety Engineers will think the situation has improved and no further action will be taken, whereas in reality it is needed.

(d)

Type II error: Fail to reject a False Null Hypothesis.

Suppose in reality: There is improved visibility due to new signs in place of old signs. Due to hypothesis testing, Highway Safety Enginners wrongly conclude that : There is no improved visibility due to new signs in place of old signs. Type II Error is committed in this situation.

(c) Real world consequence if a Type II error occurred:

Highway Safety Engineers will think the situation has not improved and they will take further action , whereas in reality it is not needed.