A manufacturer is trying to decrease the defective rate of water filters employed in refrigerators. The current failure rate = 4%. In the new version the seal was changed; 300 filters were subjected to testing as well as seven (7) failed.
Let p denote the probability of failure for new design.
Conduct the test of superiority. That is, state and test hypothesis to find if the fail rate of the new design is lower than 4%. Employ a 5% level of significance, also compute the p-value.