4. In an experiment, there are 250 trials and each trial results in a success or a failure.
- Write down two other conditions needed to make this into a binomial experiment.
It is claimed that \(10 \%\) of students can tell the difference between two brands of baked beans. In a random sample of 250 students, 40 of them were able to distinguish the difference between the two brands.
- Using a normal approximation, test at the \(1 \%\) level of significance whether or not the claim is justified. Use a one-tailed test.
- Comment on the acceptability of the assumptions you needed to carry out the test.