Transcript BA 275, Fall 1998 Quantitative Business Methods

BA 275
Quantitative Business Methods
Agenda
 Statistical Inference


Hypothesis Testing: Proportion
The p-value Approach
Computer Project #2 is due on Monday, 2/27/06.
Midterm Examination #2: Wednesday 3/1/06.
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Midterm Examination #2
 Wednesday, 3/1/06 in class.
 Closed books/notes/packet/friends exam, but I will
provide you
 The normal and the T tables
 The formulas on pp. 13, 14, and 17.
 Need a good night sleep and a calculator that
WORKS!
 Topics:



The Normal Distribution and the Central Limit Theorem
Confidence Interval Estimation, Margin of Error, Sample Size
Determination
Hypothesis Testing, the p-value approach
 CyberStats: B-11, B-12, C-1, C-2, C-3, C-4, C-6, C-7,
C-8.
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Quiz #5
Question 1. A survey of community banks asked about the loan-to-deposit (LTD) ratio, a
bank’s total loans as a percent of its total deposits. The mean LTD ratio for the 20 banks in the
sample is 76.7 and the standard deviation is 12.3. Give a 99% confidence interval for the mean
LTD ratio for community banks.
LCL (lower confidence limit)
UCL (upper confidence limit)
X  t / 2
s
n
d . f .  n  1  20  1  19
12.3
20
12.3
UCL : 76.7  2.861
20
LCL : 76.7  2.861
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Quiz #5
Question 2. “Does work stress have a negative impact on your personal life?” A sample of 100
restaurant employees was selected and 55 of them responded “Yes.” Estimate with 95%
confidence the population proportion of all restaurant employees who think that work stress has a
negative impact on their personal lives.
LCL (lower confidence limit)
UCL (upper confidence limit)
pˆ 
pˆ  z / 2
pˆ (1  pˆ )
n
55
 0.55
100
0.55(1  0.55)
LCL :0.55  1.96
100
0.55(1  0.55)
UCL : 0.55  1.96
100
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Quiz #5
Question 3.
Question
Circle one answer
If the sample mean increases, how does the width of the
confidence interval change?
Increase
Decrease
Remain the same
If the sample size is increased, how does the width of
the confidence interval change?
Increase
Decrease
Remain the same
If the confidence level is increased, how does the width
of the confidence interval change?
Increase
Decrease
Remain the same
If the sample standard deviation increases, how does
the width of the confidence interval change?
Increase
Decrease
Remain the same
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Central Limit Theorem
 In the case of sample mean
X ~ N ( ,

2
n
)
X 

n
 In the case of sample proportion
p (1  p )
pˆ ~ N ( p,
)
n
 pˆ 
p(1  p)

n
pˆ (1  pˆ )
n
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Formulas for the Proportion (formula 3
on p.13 and p.17)
100(1-a)% confidence interval estimator (p.13)
pˆ (1  pˆ )

p  z / 2
n
Hypothesis testing H0: p = p0 (p.17)
z
pˆ  p0
p0 (1  p0 )
n
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Example
4 out of 5 dentists recommend Oral-B.
Scenario 1: “Hmm, I thought it was higher.”
Scenario 2: “No, it cannot be. It should be lower.”
Scenario 3: “Really? I don’t think so.”
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Example
 A manufacturer of alkaline batteries wants to
be reasonably certain that fewer than 5% of
its batteries are defective. Suppose 300
batteries are randomly selected from a very
large shipment; each is tested and 10
defective batteries are found. Does this
provide sufficient evidence for the
manufacturer to conclude that the fraction
defective in the entire shipment is less than
0.05? Use  = 0.01.
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Example
 Three politicians are attempting to win the
Democratic nomination for senator.
 The result of a survey of 1000 Democrats is
summarized below.
 Q1. Do we have enough evidence to indicate that
Candidate A will receive more than 50% of the vote?
 Q2. If so, by how much?
Candidate A
550
Candidate B
300
Candidate C
150
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Statistical Inference Using
Statgraphics
 With only summary statistics (e.g., given the
sample mean, sample std, and sample size.)
 With only raw data (e.g., the CEO data)
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