Question 776317
<pre>
It's complete enough to know what you mean.

H0
&#956; = 40
 H1
&#956; < 40
<pre>
If the mean really is 40 with the standard deviation of 12.5
 then we find the probability that 38.7 would be that low or
lower, and if it's less than 5% of the time, it's too unlikely
and we'll reject the null hypothesis, but if it's not we won't.

Calculate the z-score:

<span style="text-decoration: overline">x</span> - <font face="symbol">m</font>   38.7 - 40
————— = ————————— = -.7353910524
  {{{sigma/sqrt(n)}}}       {{{12.5/sqrt(50)}}}

1. The first way you have to know the cut off points for the
various alpha error values.

In the case of a left one-tail test with alpha = 0.05 you have to 
have the cut-off point of -1.64, for that's the value that has 0.05 
of the area to the left of it.

2. The second way you find the p-value, which is the area to the
left of the z-score -.735  which is 0.2312, which is higher than
0.05. 

When the p-value is high, the null must fly.
When p-value is low, the null must go

Here the p-value is high, so the null must fly, so we fail to reject 
the null hypothesis.

Edwin</pre>