It's complete enough to know what you mean.
H0
μ = 40
H1
μ < 40
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:
x - m 38.7 - 40
————— = ————————— = -.7353910524
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
