# Really good intro to one-tailed hypothesis testing?

#### jjz

##### New Member
Hi,

Can anyone point me to a really clear, basic, complete, step-by-step explanation of how to do a one-tailed hypothesis test?

I got as far as calculating z:

z = (x bar - population mean) / (std dev / sqrt(n))

...but I just don't understand how to figure out what the critical values are. All the explanations I've found -- including my textbook! -- seem to leave this part out.

Thanks for any help...

#### vinux

##### Dark Knight
Hi,

Can anyone point me to a really clear, basic, complete, step-by-step explanation of how to do a one-tailed hypothesis test?

I got as far as calculating z:

z = (x bar - population mean) / (std dev / sqrt(n))

...but I just don't understand how to figure out what the critical values are. All the explanations I've found -- including my textbook! -- seem to leave this part out.

Thanks for any help...
Is your doubt specific to one-tailed hypothesis test?
If you know how to calculate critical values for two sided test, then it will be easy.
For a given confidence level( usually 95% ie alpha = 0.05) we calculate critical value such that

two sided
P[ |Z| > critical value] = alpha
where Z is the test statistic
{ for large sampel size (>30), it will be normal) }
for one sided (right tailed)
P[ Z > critical value] = alpha

If you want in more detail, give a specific example

#### jjz

##### New Member
Critical values

Thanks, Vinux. Unfortunately, I don't know how to get the critical values for a two-tailed test, either.

Here's the specific example I'm working on:

A sample of 20 customers bought books. x (bar) = $315.40, s =$43.20.

H0: the population mean <= $300 at 0.10 level of significance (then also at 0.05 level of significance) Thanks again for any help! Last edited: #### vinux ##### Dark Knight Thanks, Vinux. Unfortunately, I don't know how to get the critical values for a two-tailed test, either. Here's the specific example I'm working on: A sample of 20 customers bought books. x (bar) =$315.40, s = $43.20. H0: the population mean <=$300 at 0.10 level of significance

(then also at 0.05 level of significance)

Thanks again for any help!
Here the test statistic is  xbar = $315.40, s =$43.20 n = 20 u0 = 300
and the hypothesis is
H0: the population mean <= $300 Vs H1:he population mean >$300

so t = (315-300)/(43.20/20) =6.9444

and for alpha= 0.10 and df 20-1 =19
talpha = 1.32778 ( Use table. If the table is for two sided, then take alpha =0.20. )
this we will get using excel, use this function TINV(0.2,19) ( since this gives the two sided )

and for alpha =0.05 talpha =1.73

Both the cases t > talpha.

So we reject the hypothesis.

Rgds
VinuX

#### jjz

##### New Member
Thank you!

At last, I get it. Thank you!

Just to be sure, I think when you wrote

t = (315-300)/(43.20/20) =6.9444

...you meant

t = (315-300)/(43.20/SQRT(20)) = 1.5942

Is that right?