Math- correlation and regression?

Question

the DOT claims that there si a significient difference between the rates of emissions failures for commericial vehicles at two different privately owed but licensed centers. Among 400 tests at fast test, 26% failed while among 370 tests at rapid test, 20% failed. identify the proper conclusion at lower case sigma = 0.05

what is the correct conclusion:

a. the data support the claim p1 is not equal to is different from p2

b. the data do not support the claim p is not equal to is different from p2

Answer 1

This isn't a correlation or a regression problem. It can be best solved using a Chi-square test.  With a chi-square test, you can estimate the probability that "Fast Test" and "Rapid Test" have the same failure rate.  

Check out this site for info:

http://en.wikipedia.org/wiki/Chi-square_...

Fast Test: 104 failures, 296 success, 400 total

Rapid Test: 74 failure, 296 success, 370 total

From this, you can compute the average expected failure rate (178/770).  From this, you can calculated the expected frequency of failures at the two tests: (roughly 92 and 86).  From this, you can calculate the difference between actual and expected.  The sum of these differences, squared and divided by the expected amount (see the wiki for an illustration of this;  Its hard to explain without a figure) gives you a chi-square value.  Check this value against a chi-square table with 1 degree of freedom, and you know whether or not to support the claim that "Fast Test" and "Rapid Test" have the same underlying failure rate.

Good luck with your homework!