Chapter 11 Inferences on Two Samples
Ch 11.1 Inference about Two Population Proportions
Objective A : Distinguish between Independent and Dependent Sampling
Example 1:
Determine whether each sampling method is independent or dependent.
(a) Test scores of the same students in English and Math.
(b) The effectiveness of two different diets on two different groups of
individuals.
Objective B : Test Hypotheses or Confidence Intervals Regarding Two Proportions from
Independent Samples
Example 1:
The drug Prevnar is a vaccine meant to prevent certain types of bacterial
meningitis. It is typically administered to infants starting around 2 months
of age. In randomized, double-blind clinical trials of Prevnar, infants were
randomly divided into two groups. Subjects in group 1 received Prevnar,
while subjects in group 2 received a control vaccine. After the second dose,
137 of 452 subjects in the experimental group (group 1) experienced drowsiness
as a side effect. After the second dose, 31 of 99 subjects in the control group
(group 2) experienced drowsiness as a side effect. Does the evidence suggest
that a lower proportion of subjects in group 1 experienced drowsiness as a side
effect than subjects in group 2 at the   0.05 level of significance?
(a) Setup
(b) P  value
(c) Conclusion
Example 2:
The body mass index (BMI) of an individual is one measure that is used to
judge whether an individual is overweight or not. A BMI between 20 and
25 indicates that one is at a normal weight. In a survey of 750 men and 750
women, the Gallup organization found that 203 men and 270 women were
normal weight. Construct a 90% confidence interval to gauge whether there
is a difference in the proportion of men and women who are normal weight.
Interpret the interval.
Ch 11.2 Inference about Two Means: Dependent Samples
Objective A : Test Hypotheses or Confidence Intervals about the Population Mean
Difference of Matched-Pairs Data
Example 1:
In an experiment conducted online at the University of Mississippi, study
participants are asked to react to a stimulus. In one experiment, the
participant must press a key on seeing a blue screen. Reaction time (in
seconds_ to press the key is measured. The same person is then asked
to press a key on seeing a red screen, again with reaction time measured.
The results for six randomly sampled study participants are as follows:
(a) Why are these matched-pairs data?
(b) Is the reaction time to the blue stimulus different from the reaction
time to the red stimulus at the   0.01 level of significance?
Note: A normal probability plot and boxplot of the data indicate that
the differences are approximately normally distributed with no outliers.
(c) Construct a 99% confidence interval about the population mean difference.
Interpret your results.
Ch 11.3 Inference about Two Means: Independent Samples
Objective A : Test Hypotheses or Confidence Intervals regarding the Difference of Two
Independent Means
Example 1:
Example 2:
Ch 11.4 Inference about Two Population Standard Deviations
Objective A : Fisher’s F  distribution
Objective B : Test Hypotheses regarding Two Population Standard Deviations
Example 1:
Assume that the populations are normally distributed.
Example 2: