Determine the critical region and the critical values used to test the following

Question

Determine the critical region and the critical values used to test the following null hypotheses. (Assume a Z-test statistic is appropriate here.)

(a) H0: = 55 (), Ha: < 55, = 0.05

---Select--- less than or equal to greater than or equal to at least as extreme as at most as extreme as  

---sign--- + - ±

(b) H0: = 85 (), Ha: < 85, = 0.02

---Select--- less than or equal to greater than or equal to at least as extreme as at most as extreme as  

---sign--- + - ±  

(c) H0: = 113, Ha: 113, = 0.01

---Select--- less than or equal to greater than or equal to at least as extreme as at most as extreme as  

---sign--- + - ±  

(d) H0: = 17.6 (), Ha: > 17.6, = 0.1

---Select--- less than or equal to greater than or equal to at least as extreme as at most as extreme as  

---sign--- + - ±

Explanation / Answer

Solution:-

(a) H0: = 55 (), Ha: < 55, = 0.05

zcrituical = - 1.645

(b) H0: = 85 (), Ha: < 85, = 0.02

zcrituical = - 2.05

(c) H0: = 113, Ha: 113, = 0.01

zcrituical = + 2.575

(d) H0: = 17.6 (), Ha: > 17.6, = 0.1

zcrituical = + 2.33

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