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

dkishore1

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 2426 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 zcritical value of 1.285?
Thanks for any direction you can provide!

Dapper425

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.

meghanjackson

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!

John10

Thanks amalj
@mkytz15
Also remember that the probability of having 10% of values on the right tail is EXACTLY the same as having 10% of values in the left tail because of symmetry. So this z value of 1.285 signifies that 10% of values lies in the lower left tail also. If your test statistic falls below this value, it basically means that the mean of the population is getting further and further down from 50 and the case for rejecting the null hypothesis is really strong. (Null hypothesis claims that population mean is greater than or equal to 50)
In our case, the test statistic doesnt fall below 1.285 and so null cannot be rejected.
Hope this helps.

mar350

thanks for your help ravinsu and amalj!