A random sample of 17 observations from the population N ( , 2 ) yields the sample mean x 6 73 and the sample variance s 2 1 23 At the 1 significance level, test the following hypotheses by obtaining critical values (a) H 0 6 vs H 1 6 (b) H 0 6 vs H 1 6 (c) H 0 6 vs H 1 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

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Question: A random sample of 17 observations from the population N ( , 2 ) yields the sample mean x = 6 . 73 and the

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.

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

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