# Chapter10 Class Notes

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CHAPTER 10:
TWO-SAMPLE TESTS AND ONE-WAY ANOVA
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CRITICAL VALUE METHOD FOR DETERMINING SIGNIFICANCE

Critical Value Method                                  Critical Value Method
Two-Tailed Test                                        One-Tailed Test (Upper)

Example                                                Example
tCRITICAL values = -2.06 and +2.06                     tCRITICAL value = +2.06
tSTAT = -3.0   [Greater than 2.06, so Reject Null]     tSTAT = -3.0   [Reject Null]
tSTAT = -.75   [Between Crit values; Do Not Reject]    tSTAT = -.75   [Do Not Reject Null]
tSTAT = 2.0    [Between crit values; Do Not Reject]    tSTAT = 2.0    [Do Not Reject Null]
tSTAT = -3.0   [Less than -2.06, so Reject Null]       tSTAT = -3.0   [Do Not Reject Null]

P-VALUE METHOD FOR DETERMINING SIGNIFICANCE

2-Value Method                                         2-Value Method
Two-Tailed Test                                        One-Tailed Test (Upper)

αCRITICAL = 0.05                                       αCRITICAL = 0.05
If p-value is low (compared to α), the null must go.   If p-value is low (compared to α), the null must go.
.01 < .05      [Reject the null hypothesis]            .01 < .05      [Reject the null hypothesis]
.06 > .05      [ Do Not Reject the null hypothesis]    .06 > .05      [ Do Not Reject the null hypothesis]
.65 > .05      [Do Not Reject the null hypothesis]     .65 > .05      [Do Not Reject the null hypothesis

NOTE: BOTH METHODS WILL LEAD TO THE SAME STATISTICAL CHOICE
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EXCEL DATA ANALYSIS
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COMPARING TWO SAMPLE MEANS WITH EQUAL VARIANCE (δ 2 )
H0: µTAKWA = µRONDO
H1: µTAKWA ǂ µRONDO

ABS(t value) = 1.1825 < 2.08593; Do not reject
p-Value = .0.251361 > .05; Do not reject
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COMPARING TWO SAMPLE MEANS WITH EQUAL VARIANCE (δ 2 ): ONE-TAILED TEST
H0: µTAKWA >= µRONDO
H1: µTAKWA < µRONDO

ABS(tSTAT) = 2.4004 > 1.724718; Do not reject
p-Value = .0.013113 > .05; do not reject
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COMPARING TWO SAMPLE MEANS WITH UNEQUAL VARIANCE (Δ 2 )
H0: µTAKWA = µRONDO
H1: µTAKWA ǂ µRONDO

ABS(tSTAT) = 1.18125 > 2.085963; Reject the null.
p-Value = .0.013113 < .05; Reject the null.
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PAIRED T TESTS
H0: µA = µB
H1: µA ǂ µB

ABS(tSTAT) = 6.67799 > 2.085963; Reject the null.
p-Value = 9.08/100000 < .05; Reject the null.
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COMPARING THE PROPORTIONS OF TWO INDEPENDENT POPULATIONS

THE SITUATION

Are you likely to use this hotel again?

Beachcomber: 163/227 guests said “Yes.” p1 = 0.7181

Windsurfer: 154/262 guests said “Yes.” p2 = 0.5878

HYPOTHESES

H0: π1 = π2

H1: π1 ǂ π2

α = 0.05, so ZCRITICAL = ±1.96

TEST STATISTIC

Set (π1-π2) to 0

IS THE TEST STATISTIC GREATER THAN Z C R I TI C A L ?
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F-TEST FOR THE DIFFERENCE BETWEEN TWO VARIANCES
2         2
H0: δ TAKWA   =δ    RONDO
2             2
H1: δ TAKWA   ǂδ    RONDO

F value = 1.15 < 2.97823702; Do not reject
p-Value = .41470805 > .05; do not reject
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SINGLE-FACTOR ANALYSIS OF VARIANCE
H0: µTAKWA = µRONDO = µRONDO
H1: At least one of the population means is different.

ABS(F) = 18.11688 > 3.31583; Reject the null.
p-Value = 6.93/1000000 < .05; Reject the null.

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