Question re: Elan QM practice problem critical, hypothesis, direction, practice, problems

glamorous

I've been working through some practice problems with Elan and had a question about a few problems in reading 11, hypothesis testing.

Looking at the answers to problems 24-26 in Reading 11, I'm solid getting through the test statistic but I keep getting tripped up on getting the right critical values and it throws my answer off.

If we take a look at problem 26 for example, can someone explain how they come up with a z-critical value of -1.285?

Thanks for any direction you can provide!

shootingstar

I believe Elan does a great job in explaining this concept.

In this particular problem, your

H0 : u >=50

and just think that you desperately want to reject this SOB hypothesis so that you can proudly claim that the mean of the population might be less that 50 in reality. Your only hope is the critical region where it gets rejected. At a 10% level of significance( this is one sided) ,
10% of the values of the standard normal distribution falls onto the critical region. You look in the table to find out the z value whose probability matching .01 (means 10% of the values are in the right tail- thats how the table is constructed). That happens to be -1.285

Try drawing a normal distribution and shading out the lousy region where you want the rejection to happen if the test statistic falls there. That will help.

koba

Very nice (and interesting) explanation ravinsu

mkytz15 go through the video lecture on reading 9. Their explanation of z scores and description of looking up z scores is better than my stats prof in college!