It is known from past records that 1 in 5 bowls produced in a pottery have minor defects. To monitor production a random sample of 25 bowls was taken and the number of such bowls with defects was recorded.
Using a 5\% level of significance, find critical regions for a two-tailed test of the hypothesis that 1 in 5 bowls have defects. The probability of rejecting, in either tail, should be as close to \(2.5 \%\) as possible.
State the actual significance level of the above test.
At a later date, a random sample of 20 bowls was taken and 2 of them were found to have defects.
Test, at the \(10 \%\) level of significance, whether or not there is evidence that the proportion of bowls with defects has decreased. State your hypotheses clearly.