
These WINKS statistics tutorials explain the use and interpretation of standard statistical analysis techniques for Medical, Pharmaceutical, Clinical Trials, Marketing or Scientific Research. The examples include howto instructions for WINKS SDA Version 6.0 Software. Download evaluation copy of WINKS. 
Single Sample ttest
Definition: Used to compare the mean of a sample to a known number
(often 0).
Assumptions: Subjects are randomly drawn from a population and the
distribution of the mean being tested is normal.
Test:
The hypotheses for a single sample ttest are:
H_{o}:
u = u_{0}
H_{a}:
u < > u_{0}
(where u_{0}
denotes the hypothesized value to which you are comparing a population mean)
Test
statistic: The test statistic, t, has N1 degrees of freedom, where N is
the number of observations.
Results
of the ttest: If the pvalue associated with the ttest is small
(usually set at p < 0.05), there is evidence to reject the null hypothesis
in favor of the alternative. In other words, there is evidence that the mean
is significantly different than the hypothesized value. If the pvalue
associated with the ttest is not small (p > 0.05), there is not enough
evidence to reject the null hypothesis, and you conclude that there is
evidence that the mean is not different from the hypothesized value.
Example:
Single Sample ttest
You read in
an article that an educator claimed that the average educational level for
people over 60 in was 8th grade. You happen to have a data (ELDERLY.DBF)
that contains a random sample of elderly people, and you want to test the
educator's claim. The results of performing a single sample ttest are:



Single Sample ttest



Variable Name is EDUC


N = 166 Missing or Deleted = 0

Mean = 10.07831 St. Dev (n1) = 3.25109


Null
Hypothesis: mean(POPULATION) = 8


Calculated t = 8.24 with 165 D.F. p = < 0.001 (2  sided test)


95%
C.I. about Mean is (9.57995, 10.57667)


A
low value of p supports rejection of the null hypothesis.

There is evidence that the actual mean is different from the

hypothesized mean.
Exercise
 Single Sample ttest
You have
been told that the average employee for your industry has an average
dexterity score of 100 on a standardized test. You think your employees will
score differently, so you give a random sample of 12 the test. The results
are:
Subj. Test Score
1 98
2 102
3 120
4 140
5 123
6 101
7 89
8 99
9 119
10 103
11 132
12 107
1. Perform
a single sample ttest on this data.
2. What are
your hypotheses?
3. What
conclusion do you make?
4. Use the
Detailed Statistics option to calculate a 95% confidence interval on the
mean. How does this approach differ from doing the ttest?
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