Assume s is known. What are the critical values for testing H?: µ=200 against H¹: µ ? 200 with a = 0.04 ?

Question

Assume σ is known. What are the critical values for testing Hο: µ=200 against H¹: µ ≠ 200 with α = 0.04 ?

a. ±1.41

b.±2.05

c.±1.67

d.±1.75

Answer 1

ASSUMING that (a) the underlying population is normally distributed, (b) sampling is random with replacement, and (c)  the test statistic you are using is the (standardized) sample mean, you use a two-sided test.

 

The rejection region is - z_sub_alpha/2 < (sample mean - 200) / (sigma / sqrt(sample size)) < z_sub_alpha/2.

 

You use a z-test because sigma is known,  The level of significance alpha is given to be 0.04.  For a standard normal distribution you want z_sub_ 0.02.  The two critical values are then, plus or minus z_sub_ 0.02.

 

To find z_sub_ 0.02, go to OpenOffice Calc and use the function  NORMSINV().  (If you do not know, how ask me as a comment.)  You get z_sub_ 0.02 = -2.0537. 

 

Check Answer (b) above.