Math 201

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Math 201

• 6.2 Tests of Significance ctd
• 7.1 Inferences on m

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Two-sided Tests and Confidence Intervals
For x372.5, s10 and n25 ? sx10/52
95 CI for m is (372.5-1.962,
372.51.962)(368.58, 376.42)
H0 m 368 Ha m ¹ 368
Since 368 is outside the interval, we reject H0
at a .05.
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Math 201

• Chapter 7
• 7.1 Inference for m

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What is different?

• Chapter 6 ? Assuming s known
• Confidence Interval for m
• Significance test for m
• Chapter 7 ? s is not known

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If s is Not Known?

• Substitute the sample standard deviation for s

Standard error of X
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Z Test for Mean( Known)

• Assumptions
• Population is normally distributed
• If not normal, requires large samples
• Z test statistic

Z distribution
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t Test Unknown

• Assumption
• Population is normally distributed
• If not normal, requires a large sample
• T test

t distribution with n-1 degrees of freedom
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t distribution
Table D
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CI for ( not known)

• Assumptions
• Population is normally distributed
• If population is not normal, use large sample
• C Confidence interval for m

Estimate Margin of Error
Page 517 26
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Estimation Process
Population All adult women
Random Sample n4
What the value of m?
64, 67, 61, 68 x 65
XHeight ? is unknown
Sample
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95 Level of CI
t3 curve
.95
.025
.025
-t
t
x 65 s3.16 n4
(65-3.1821.58, 653.1821.58)
Exercise 7.10
( 59.97, 70.03)
Page 513 6
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Guidelines

• Practical guidelines for inference on m
• nlt15 ? Use t if data are close to normal and no
  outliers.
• n gt15 ? Use t if no outliers or strong skewness.
• n gt40 ? Use t even for skewed distributions.

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Matched Pair Design
H
T
H
PAIR
RANDOMIZE
TREAT
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Matched pairs designs

• Compares only two treatments
• Choose two EUs that are as closely matched as
  possible
• Assign treatments randomly to each EU.
• Sometimes each pair consists of just one Subject.
• Example Coke Vs Pepsi
• ?Compare, randomization, repetition

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Example

• Weight loss program Here is an SRS of
  participants

Is the program effective?
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Is the Program Effective?

• Let m Ave wt. Loss for all participants
• H0 m0
• Ha mgt0
• Minitab
• Data for the sample of 8 participants
• ? Normal?
• ? average 8.94 lbs
• standard deviation 10.47 lbs

CI?
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HW

• Chapter 6?6.37, 6.63
• Chapter 7?7.1, 7.13, 7.37
• Quiz Friday on Chapter 6 and 7.1
• Final Project on Q drive (due May 4th)