Stats problem... need help!!!

[LoveStruck16]

I have this stats question and I'm confused on what to do, any help would be greatly appreciated.

- Determine whether an observed sample mean of 84 based upon a sample of n=25 is significantly different from a (null hypothesized) population mean of 81 with a standard deviation of 10.
a) state your hypothesis
b) state your alpha value and the critical values
c) show your calculations
d) state your decision regarding the null hypothesis

 

[tkhunny]

a1) \(\displaystyle H_{0}\): Population Mean = 81
a2) \(\displaystyle H_{a}\): Population Mean NOT= 81

Okay, you do part b).

 

[LoveStruck16]

So the alpha/critical values would be 0.05 and 0.10?

 

[tkhunny]

You pick it. It is also very important to decide what kind of test you will be performing. 1-tail? Maybe not. It goes to the nature of the question and the definition of the hypotheses. They way I defined them, it appears to be a 2-tail test. Perhaps you defined the hypotheses some other way.

 

[LoveStruck16]

K so if i do a two tail test then the critical values would be..

0.10

Thus, 1-0.10 = 0.90
0.90/2 = 0.45

Then I look at the Z-table chart in my textbook and look for .10 and the value is then 1.812 and I divide that by 2 (1.812/2=0.906)

Therefore the critical value would be 0.906? ..

I hope the way i explained it wasn't confusing...

 

[tkhunny]

1) That seems a little odd. Normally, one would work with the tail area. Certainly it would depend on how your table is designed.
2) Are you sure a Sample Size of 25 is big enough to use a z-score? Maybe a t-score would be more appropriate?

What say you?