A student, asked to give a class demonstration of the use of an ordinary t-statistic confidence interval for comparing two means in a single factor study with 5 levels, proposed to construct a 99% confidence interval for the pairwise comparison of ? 3 with ? 5 , stating that this particular comparison had been chosen because the estimated treatment means Y3. and Y5. were the largest and smallest respectively. The student went on to say "This confidence interval is particularly useful. If it does not straddle zero, it indicates, with significance level ? = .01, that the factor level means are not equal.
a) Explain why the student's assertion is not correct.
b) How should the confidence interval be constructed so that the assertion can be made with significance level ? = .01?