1. Statistical Inference: One- Sample Confidence Interval
Chapter 11
Statistical Inference: One-
Sample Confidence Interval
I Criticisms of Null Hypothesis Significance
Testing
 Does not indicate whether the effect is large or
small

2.  A confidence interval for  is a segment on the
 Answers the wrong question: Prob(D|H0). The
correct question concerns Prob(H0|D).
 Is a trivial exercise; all null hypotheses are false.
 Turns a continuum of uncertainty into a reject-do-
not reject decision.
II Confidence Interval for 
 A confidence interval for  is a segment on the
real number line such that that  has a high
probability of lying on the segment.

3. Figure 1. Sampling distribution of t. If one t statistic is randomly
sampled from this population of t’s, the probability is .95 that the
obtained t will come from the interval from –t.05/2,  to t.05/2, .

4. 1. From Figure 1, the following probability statement
follows:
2. Replacing t with and using
some algebra gives the following 100(1 – )%
two-sided confidence interval for  L1 L2

5. 3. L1 and L2 denote, respectively, the lower and
upper endpoints of the open confidence interval
for .
4. A researcher can be 100(1 – )% confident that 
is greater than L1 and less than L2.
5. The probability (1 – ) is called the confidence
coefficient and is usually equal to (1 – .05 ) = .95.

6. 1. Consider the following hypotheses for the
6. The assumptions associated with a confidence
interval are the same as those for a one-sample t
statistic.
A. Computational Example: Two-Sided Interval
1. Consider the following hypotheses for the
Idle-On-In College registration example:
H0:  =0
H1:  ≠ 0

7. 2. A two-sided 100(1 – .05) = 95% confidence
interval for , where

8. 3. The dean can be 100(1 – .05) = 95% confident
that  is greater than 2.78 and less than 3.02.
4. The dean can be even more confident that  lies
in the interval from L1 to L2 by computing a
100(1 – .01) = 99% confidence interval.

9. 5. A two-sided 100(1 – .01) = 99% confidence
interval for , where t.01/2, 26 = 2.779, is given by

10. 6. Graphs of the two confidence intervals
95% confidence interval for 
99% confidence interval for 

11. B. More On the Interpretation of Confidence Intervals
7. As the dean’s confidence that she has captured 
increases, so does the size of the interval from L1
to L2.
B. More On the Interpretation of Confidence
Intervals
C. Computational Example: One-Sided Interval
1. Suppose that one-tailed hypotheses, H0:  ≥0
and H1:  <0, reflect the dean’s hunch about
the new registration procedure.

12. 2. A one-sided 100(1 – .05) = 95% confidence
interval for , where

13. 3. Comparison of one- and two-sided confidence
intervals
One-sided 95% confidence interval for 
Two-sided 95% confidence interval for 

14. Over Hypothesis Testing
D. Advantages of Confidence Interval Estimation
Over Hypothesis Testing
1. Hypothesis testing is not very informative. A
confidence interval narrows the range of possible
values for .
2. Confidence intervals can be used to test all null
hypotheses such as H0:  =0. Any 0 that lies
outside of the confidence interval corresponds to a
rejectable null hypothesis.

15. 3. A sample mean and confidence interval provide
an estimate of the population parameter and a
range of values—the error variation—qualifying
the estimate.
4. A 100(1 – )% confident interval for  contains
all of the values of 0 for which the null
hypothesis would not be rejected.

16. III Practical Significance
A. Estimator of Cohen’s d
1. Hedges’s g for the registration example
2. Interpretation of g   

17. 3. Computation of g from t statistics in research
reports
4. For the registration example, t = and n = 27