Hypothesis Testing and Confidence Intervals for Proportions and
Hypothesis Test for Difference between Two Means
A pharmaceutical company is testing a new cold medicine to
determine if the drug has side affects. To test the drug, 8
patients are given the drug and 9 patients are given a placebo
(sugar pill). The change in blood pressure after taking the pill
was as follows:
Given drug: 3 4 5 1 -2 3 5 6
Given placebo: 1 -1 2 7 2...
10.4: Inferences About the Difference Between Two Population
Proportions
In a test of the quality of two television commercials, each
commercial was shown in a separate test area six times over a
one-week period. The following week a telephone survey was
conducted to identify individuals who had seen the commercials.
Those individuals were asked to state the primary message in the
commercials. The following results were recorded.
Commercial A
Commercial B
Number Who Saw Commercial
155
204
Number Who Recalled...
This chapter extends the hypothesis testing to analyze
difference between population proportions based on 2 or more
samples, and to test the hypothesis of independence in the joint
responses to 2 categorical variables. Can we provide a real world
example for using the Chi-square test along with expectation of the
outcomes?
test the hypothesis (α = 0.05) that the population proportions
of red and brown are equal (pred = pbrown). You are testing if
their proportions are equal to one another. NOTE: These are NOT
independent samples, but we will use this approach anyway to
practice the method. This also means that n1 and n2 will both be
the total number of candies in all the bags. The “x” values for red
and brown are the counts of each we found...
In a test for the difference between two proportions, the sample
sizes were n1 = 120 and n2
= 85, and the numbers of events were x1 = 55
and x2 = 45. A test is made of the hypotheses
H0: p1 =
p2versus H1:
p1 ≠ p2.
Compute the value of the test statistic.
Can you reject H0 at the α = 0.05
level of significance?
Can you reject H0 at the α = 0.01
level of significance?
Using the Chi-Square test for the difference between two
proportions, determine (?=0.05) if there is a difference in
population proportion between male patients using Medicare as their
Payer versus female patients using Medicare as their Payer. Be sure
to set up the null and alternate hypotheses.
Using the Patients dataset, determine if there is a relationship
between length of stay and total charges. Your answer should
include the following:
Scatter Plot
Linear Regression Equation (with interpretation)
Coefficient of Determination (with...
Comparisons of two population proportions when the hypothesized
difference is zero
Carry out a two-tailed test of the equality of banks’ share of the
car loan market in
1980 and 1995.
Population 1: 1980
n1 = 1000
x1 = 53
? 1 = 0.53
Population 2: 1985
n2 = 100
x2 = 43
? 2= 0.53
Find the value of z that would be used to test the
difference between the proportions, given the following. (Use G -
H. Give your answer correct to two decimal places.)
Sample
n
x
G
372
312
H
423
326
Comparing two population proportions.
We expect that there is no
difference in proportion of status of employment between male and
female recent business graduates.
a) insert a frequency table
and a bar chart or a pie chart labeled properly. USING
EXCEL
b) Perform hypothesis test: Calculate the P-value and make the
conclusion (reject or fail to reject Ho). Insert Excel
software output.
C)
Calculate the corresponding confidence interval and check if the
conclusion is the same
Status
Gender
Part-time
F...