A random sample of 17 observations from the population N(, ²) yields the sample mean x= 6.73 and the sample variance s²= 1.23. At the 1% significance level, test the following hypotheses by obtaining critical values:

(a) H₀: = 6 vs. H₁: >6.

(b) H₀: = 6 vs. H₁: <6.

(c) H₀: = 6 vs. H₁: 6= 6.

Repeat the above exercise with the additional assumption that ²= 1.23. Compare the results with those derived without this assumption and comment.