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T-Test
(Hypothesis test for small sample sizes)
Find the critical value for
• Left tail, n = 15
  0.05
t0  1.761
Find the critical value for
• Right tailed ; n = 10
  0.01
t0  2.821
Find the critical value for
• Two-tailed, n = 28
  0.02
t0  2.473
t0  2.473
Assumptions:
• SRS (Simple Random Sample)
• The population is normally or
approximately normally distributed
• Population Standard deviation is unknown
and n < 30
The Standardized test statistic t
is:
x
t
s/ n
Example:
• The American Automobile Association
claims that the mean nightly lodging rate for
a family of four traveling on vacation in
California is at least $136. A random
sample of eleven such families has a mean
nightly lodging rate of $126 with a standard
deviation of $12. Is there enough evidence
to reject the claim at   0.10 ? Assume the
population is normally distributed.
• a) Write the null and alternative
hypothesis mathematically and identify the
claim
H0
Ha
  $136
:   $136
:
(claim)
• Find the critical values and identify the
rejection region
1.372
Find the standardized test statistic
126  136
t
12 / 11
= -2.76
Conclusion
• Decide whether to reject or fail to reject the
null hypothesis. Then interpret the decision
in the context of the original claim.
At the 10% level, reject the null hypothesis.
Evidence does not supports the claim that the
mean daily meal cost is greater than or equal to
$136.
Now do
Practice
7.3