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, = 0.1

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

(b)

H0: = 95 (),

Ha:

< 95, = 0.05

---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, = 0.02

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

(d)

H0: = 19.4 (),

Ha:

> 19.4, = 0.01

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

Explanation / Answer

(a)The test is left tailed.

For =0.01, the critical values are -2.58.

Reject the null hypothesis if the test statistic falls in the critical region that is if z obtained<-2.58.

(b) The test is left tailed.

For =0.05, the critical values are -1.96.

Reject the null hypothesis if the test statistic falls in the critical region that is if z obtained<-1.96.

(c) The test is both tailed.

For =0.02, the critical values are +/-2.33.

Reject the null hypothesis if the test statistic falls in the critical region that is if z obtained<-2.33 or z obtained>+2.33.

(d) The test is right tailed.

For =0.01, the critical values are +2.58.

Reject the null hypothesis if the test statistic falls in the critical region that is if z obtained>+2.58.

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