Download Chapter 7 Section 2

Chapter 7 Section 2
Comparing Two Means
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We want to compare…
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Each group is considered…
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Responses in each group are…
2-Sample T-test
Same steps for the test of significance:
1.
2.
3.
4.
2 populations with each of their statistics and parameters…
Pop. 1
population mean
population std. dev.
sample size
sample mean
sample std. dev.
Pop. 2
(denoted with numbers)
Hypotheses:
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Are comparing…
Ho:
Ha:
Test Statistic:
t=
P-Value:
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Degrees of freedom:
o
o (Textbook, p. 549)
Conclusion:
Almost the same 2 sentences…
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Calculator:
OR
2-Sample T-Interval
Formula:

Degrees of Freedom:
Calculator:
Assumptions (for both 2-sample test and interval)
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Example:
We are trying out a new teaching style that we think will increase test scores. Below is the
data for both the treatment and control groups.
Treatment
Control
n
21
23
x
81.48
77.85
s
8.12
7.98
Test these hypotheses
Create and interpret a 95% confidence interval
AP Statistics: Section 7.2 – Two Sample t-Procedures
1. A 30-month study (randomly chosen months) is conducted to determine the difference in the
numbers of accidents per month occurring in two departments in an assembly plant. Suppose the
first department averages 12.3 accidents per month with a standard deviation of 3.5, while the
second averages 7.6 accidents with a standard deviation of 3.4. Determine a 95% confidence
interval estimate for the difference in the numbers of accidents per month.
2. A survey is run to determine the difference in the cost of groceries in suburban stores versus inner
city stores. A preselected group of items is purchased in a sample of 45 suburban and 35 inner city
stores. Find a 90% confidence interval estimate for the difference in the cost of groceries.
Suburban
n = 45
x  $36.52
s = $1.10
Inner City
n = 35
x  $39.40
s = $1.23
3. An experiment is performed to determine whether the average nicotine content of one kind of cigarette (1)
significantly exceeds that of another kind (2). Test the hypothesis at the .05 level of significance.
n
Cigarette 1
Cigarette 2
50
40
x
2.61
2.38
s
0.12
0.14
4. A study of the number of business lunches that executives in the insurance and banking industries claim as
deductible expenses per month was based on random samples and yielded the results in the table.
Determine at the 0.05 level of significance whether the mean for insurance is different than the mean of
banking.
n
Insurance
Banking
40
50
x
9.1
8.0
s
1.9
2.1