After each government project is completed, the concerned department inspects the project and given a “pass” or “fail” rating. A pass rating is necessary before the appropriate contractor is given the final payment. A failed project must be reinspected until it passes the inspect. The reinspection is both costly and time-consuming. In order to deter failure, the government decided to publicize the inspection records of all contracts. 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. Test whether there is sufficient evidence to conclude that public web access to the inspection records has increased the proportion of projects that passed on the first inspection by more than 5 percentage points. Use α=0.10. Perform hypothesis test using: a) Critical Value Approach b) P-value Method c) Using Confidence Interval Total samples % pass on first inspection With public access (after) 400 68% Without Public access (before) 200 81%
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
After each government project is completed, the concerned department inspects the project and given a “pass” or “fail” rating. A pass rating is necessary before the appropriate contractor is given the final payment. A failed project must be reinspected until it passes the inspect. The reinspection is both costly and time-consuming. In order to deter failure, the government decided to publicize the inspection records of all contracts. 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.
Test whether there is sufficient evidence to conclude that public web access to the inspection records has increased the proportion of projects that passed on the first inspection by more than 5 percentage points. Use α=0.10.
Perform hypothesis test using:
a) Critical Value Approach
b) P-value Method
c) Using Confidence Interval
|
|
Total samples |
% pass on first inspection |
|
With public access (after) |
400 |
68% |
|
Without Public access (before) |
200 |
81% |
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