Question

The department of code enforcement of a county government issues permits to general contractors to work on residential projects. For each permit issued, the department inspects the result of the project and gives a “pass” or “fail” rating. A failed project must be re-inspected until it receives a pass rating. The department had been frustrated by the high cost of re-inspection and decided to publish the inspection records of all contractors on the web. It was hoped that public access to the records would lower the re-inspection rate. A year after the web access was made public, two samples of records were randomly selected. One sample was selected from the pool of records before the web publication and one after. The proportion of projects that passed on the first inspection was noted for each sample. The results are summarized below. Construct a point estimate and a 90% confidence interval for the difference in the passing rate on first inspection between the two time periods. No public web access n1=500 320 Public web access n2=100 80

Answer 1

.

We know that

we know that

(a) POINT ESTIMATE:

INTERVAL ESTIMATE:

90% Confidence Interval of is

Where

Since Confidence Interval = 90%

So = 10% = 0.10

Therefore

Therefore the 90% Confidence Interval of   is

NOTE(1);

S.E means Standard Error

Means Marginal Error

means Critical value of Z

NOTE(2) : To See the Critical Values of Z; we use the Standard Normal area tabulated values which i posted below.

How to see?

If alpha = 10% the confidence interval = 90%

Divide the value 90 with 100. you will get 0.90 and after that divide the value 0.90 with 2; you will get 0.45. Now Search this 0.45 in side the table ( repeating again see inside the table). You will find this at the intersection of (1.6, 0,04) which is Zcri value i.e 1.645.

Like this you can find the Zcri for any alpha values.