Order WINKS 7   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 how-to instructions for WINKS SDA Version 6.0 Software. Download evaluation copy of WINKS.

Single Sample t-test

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 t-test are:

H_o: u = u₀

H_a: u < > u₀

(where u₀ denotes the hypothesized value to which you are comparing a population mean)

Test statistic: The test statistic, t, has N-1 degrees of freedom, where N is the number of observations.

Results of the t-test: If the p-value associated with the t-test 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 p-value associated with the t-test 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 t-test

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 t-test are:

   -------------------------------------------------------------------

   Single Sample t-test                              

   -------------------------------------------------------------------

   Variable Name is EDUC

 

   N         =    166                Missing or Deleted = 0

   Mean      = 10.07831                   St. Dev (n-1) = 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 t-test

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 t-test 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 t-test?

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