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

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1 Answer

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.