Chapter 11 Inferences on Two Samples

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 level of significance?

(a) Setup

(b) value

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 level of significance?
Note: A normal probability plot and boxplot of the data indicate that
the differences are approximately normally distributed with no outliers.

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: