Hypothesis Tests – Some Examples
Example 1
:
Directional hypothesis test for a population mean.
The U. S. Food and Drug Administration recommends that individuals consume 1000 mg of
calcium daily.
The International Dairy Foods Association (IDFA) sponsors and advertising
campaign aimed at male teenagers to try to increase calcium consumption.
After the campaign, the
IDFA obtained a random sample of 50 male teenagers and found that the mean amount of calcium
consumed was
=
x
1081 mg, with a standard deviation of s = 426 mg.
Conduct a test to determine
whether the campaign was effective.
Use the
α
= 0.05 level of significance.
We want to prove that the mean,
μ
, calcium consumption for male teenagers is greater than
the FDA recommendation of 1000 mg per day.
Hence,
Step 1
:
H
0
:
μ
≤
1000 mg.
versus
H
a
:
μ
> 1000 mg.
Note that the alternative hypothesis states what we are trying to prove; the null hypothesis
states the opposite.
Step 2
:
n = 50,
α
= 0.05
Note that in the real world, we would decide on a value for
α
based on our examination of
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 Fall '10
 Staff
 Statistics, Null hypothesis, Statistical hypothesis testing, great deal, IDFA, male teenagers

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