BUSMGT 2320 Lecture 4: 4. Lecture 4  One Sample T; Paired Samples T
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t○
Test statistic•
t , t , t○
Critical Value (Point)•
Matched (paired) samples•
Notation:
Estimate with s, giving•
No longer Standard Normal Z, no longer Zscores•
Assuming is Normally distributed, result is now a t random variable•
Still measures # of standard deviations from mean•
Substituting s for : Student's t
In the onesample case○
df = # of observation used to calculate sum of squared deviations  $ of
mathematical restrictions
○
There is a family of tcurves○
Has one parameter: degrees of freedom: df, DF•
The tDistribution
Same symmetric mound shape○
Same center,
○
Both asymptotic○
tcurves have fatter tails○
tcurves become taller and skinnier as df increase○
Observations:•
Comparing t to Z
m = t*s•
Symmetric case:•
Reasonable Sampling Error  Unknown
PROBLEM: average income of households within 25 miles must exceed
$50,000 for success
SRS of 64 and found average annual income of $50,725 with standard
deviation of $4200
Does this indicate > $50,000
PLAN
Hypothesis:
SRS
s = $4200
n = 64; income is usually skewed, but CLT probably applies, given n > 2(30)
n = <.1N SE( ) = no adjustment
The Unlimited Avenue Case
Lecture 4

One sample t; Paired Samples t
Thursday, February 2, 2017 06:59 PM
Unit 1 Page 1