Math- inferences from two samples?

Question

The DOT claims that there is a significiant difference between the rates of emissions failures for commercial vehicles at two different privately owned by license testing centers. Among 400 tests at fast test, 26% failed while 370 tests at rapid test, 20% failed. Identify the proper conclusion at alpha; probability of a type I error or the area of the critical region = 0.05.

what conclusion would be correct:

the data support the claim p1 = p2 or the data do not support the claim p1 = p2

Answer 1

ANSWER: DATA does not support claim p1 = p2

Why???

Two-proportion z-test, equal variances

Assumptions:

n1 p1 > 5 AND n1(1 − p1) > 5 and n2 p2 > 5 and n2(1 − p2) > 5 and independent observations

Test and CI for Two Proportions

Sample    X    N  Sample p

1       104  400  0.260000

2        74  370  0.200000

Difference = p (1) - p (2)

Estimate for difference:  0.06

95% CI for difference:  (0.000763921, 0.119236)

Test for difference = 0 (vs not = 0):  Z = 1.97  P-Value = 0.048