Question

Business sign conservation. The Federal Highway Administration (FHWA) lately issued new guidelines for maintaining and replacing business signs. Civil masterminds at North Carolina State University studied the effectiveness of colorful sign conservation practices developed to cleave to the new guidelines and published the results in the Journal of Transportation Engineering (June 2013). One portion of the study concentrated on the proportion of business signs that fail the minimal FHWA retro-reflectivity conditions. Of signs maintained by the. North Carolina Department of Transportation (NCDOT), .512 were supposed failures. Of signs maintained by. County- possessed roads in North Carolina, 328 were supposed. Failures. Conduct a test of the thesis to determine whether the true proportions of business signs that fail the minimal FHWA retro-reflectivity conditions differ depending on whether the signs are maintained by the NCDOT or by the county. Test using α = .05

Short answer

The null hypothesis is rejected at α = 0.05.

Step-by-step solution

Step-by-Step Solution Step 1: Check the true proportions of traffic signs

Check whether the true proportions of traffic signs that fail the minimum FHWA retro-reflectivity requirements differ depending on whether the signs are maintained by the NCDOT or by the county.

The test hypotheses are given below:

Null hypothesis:

H₁: P₁-P₁= 0

The true proportions of traffic signs that fall under the minimum FHWA retro-reflectivity requirements do not differ depending on whether the signs are maintained by the NCDOT or the county.

Alternative hypothesis:

$H_a:P_1-P_2\ne 0$

The true proportions of traffic signs that fall under the minimum FHWA retro-reflectivity requirements differ depending on whether the signs are maintained by the NCDOT or the county.

Use MINITAB

Use MINITAB to obtain the test statistic and p-value for the difference.

MINITAB procedure:

Step 1: Select stat > Basic Statistics > 2 proportions.

Step 2: Select Epitomized data

Step 3: In the First sample, enter Trials and Events as 512.

Step 4: In the Second sample, enter Trials and Events as 328.

Step 5: Check Perform thesis test in Hypothecated proportion, enter 0.

Step 6: Check Options and enter the Confidence position as 95.0.

Step 7: Select not equal in indispensable

Step 8: Click OK in all dialogue boxes.

Minitab Output

MINITAB output

Test and CI for Two Proportions

Difference = p (1) – p (2)

Estimate for difference: 0.184

95% CI for difference: (0.141497, 0.226503)

Test for difference = 0 (vs ≠ 0): z = 8.34 p-value = 0.00

Fisher`s exact test: p – value = 0.0000

From the MINITAB output, the value test statistic is 8.34, and the p-value is 0.0000

Rejection rule

If the p-value <a, then reject the null hypothesis.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value (=0.000) <a=0.05)

Therefore, the null hypothesis is rejected at 2 = 0.05

Thus, it can be concluded that the true proportions of traffic signs that fall under the minimum FHWA retro-reflectivity requirements differ depending on whether the signs are maintained by the NCDOT or by the county.

Final answer

The null hypothesis is rejected at α = 0.05.