91影视

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:

H鈧�: P鈧�-P鈧�= 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:

$H_a:P_1鈭�P_2鈮�0$

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 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

Test and CI for Two Proportions

Difference = p (1) 鈥� p (2)

Estimate for difference: 0.184

95% CI for difference: (0.141497, 0.226503)

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

Fisher`s exact test: p 鈥� value = 0.0000

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

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.

The null hypothesis is rejected at 伪 = 0.05.