Null & Alternative Hypothesis?

Question

What is the null & alternative hypothesis?

Test of mu = 550 vs > 550

Variable SATM

N = 25

Mean = 594

StDev = 64

T = 3.67

P = .001

Answer 1

Null hypothesis is the thing we assume to be true initially (until we can prove otherwise).

Thus, Nul. hypothesis = Ho = µ = 550

Alt. hypothesis = Ha = µ > 550

Conduct your test to see if you can reject/ fail to reject Ho and state your conclusion.

[Answer: see above]

Answer 2

Consider the hypothesis test as a trial against the null hypothesis.  the data is evidence against the mean.  you assume the mean is true and try to prove that it is not true.  After finding the test statistic and p-value, if the p-value is less than or equal to the significance level of the test we reject the null and conclude the alternate hypothesis is true.  If the p-value is greater than the significance level then we fail to reject the null hypothesis and conclude it is plausible.  Note that we cannot conclude the null hypothesis is true, just that it is plausible.

If the question statement asks you to determine if there is a difference between the statistic and a value, then you have a two tail test, the null hypothesis, for example, would be μ = d vs the alternate hypothesis μ ≠ d

if the question ask to test for an inequality you make sure that your results will be worth while.  for example.  say you have a steel bar that will be used in a construction project.  if the bar can support a load of 100,000 psi then you'll use the bar, if it cannot then you will not use the bar.

if the null was μ ≥ 100,000 vs the alternate μ < 100,000 then will will have a meaningless test.  in this case if you reject the null hypothesis you will conclude that the alternate hypothesis is true and the mean load the bar can support is less than 100,000 psi and you will not be able to use the bar.  However, if you fail to reject the null then you will conclude it is plausible the mean is greater than or equal to 100,000.  You cannot ever conclude that the null is true.  as a result you should not use the bar because you do not have proof that the mean strength is high enough.

if the null was μ ≤ 100,000 vs. the alternate μ > 100,000 and you reject the null then you conclude the alternate is true and the bar is strong enough; if you fail to reject it is plausible the bar is not strong enough, so you don't use it.  in this case you have a meaningful result.  

Any time you are defining the hypothesis test you need to consider whether or not the results will be meaningful.

Hypothesis Test for mean:

assuming you have a large enough sample such that the central limit theorem holds and the mean is normally distributed then to test the null hypothesis H0: μ = Δ

find the test statistic z = (xBar - Δ) / (sx / sqrt(n))

where xbar is the sample average

sx is the sample standard deviation

n is the sample size

The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.

H1: μ > Δ; p-value is the area to the right of z

H1: μ < Δ; p-value is the area to the left of z

H1: μ ≠ Δ; p-value is the area in the tails greater than |z|

for a small sample test for the mean every thing is the same save the test statistic is a t statistic with n - 1 degrees of freedom.  However, in this case the underlying distribution must be normal for this test to be valid.

in this case you have:

H0: μ ≤ 550 vs H1: μ > 550

with such a small p-value we reject the null hypothesis and conclude the alternate is true.