Comparing Two Sample Means with Equal Variance (Δ2): One-Tailed Test

CHAPTER 10: TWO-SAMPLE TESTS AND ONE-WAY ANOVA 2

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 3

EXCEL DATA ANALYSIS 4

COMPARING TWO SAMPLE MEANS WITH EQUAL VARIANCE (δ2)

H0: µTAKWA = µRONDO

H1: µTAKWA ǂ µRONDO 5

ABS(t value) = 1.1825 < 2.08593; Do not reject p-Value = .0.251361 > .05; Do not reject 6

COMPARING TWO SAMPLE MEANS WITH EQUAL VARIANCE (δ2): 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 7

COMPARING TWO SAMPLE MEANS WITH UNEQUAL VARIANCE (Δ2)

H0: µTAKWA = µRONDO

H1: µTAKWA ǂ µRONDO 8

ABS(tSTAT) = 1.18125 > 2.085963; Reject the null. p-Value = .0.013113 < .05; Reject the null. 9

PAIRED T TESTS

H0: µA = µB

H1: µA ǂ µB 10

ABS(tSTAT) = 6.67799 > 2.085963; Reject the null. p-Value = 9.08/100000 < .05; Reject the null. 11

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 CRITICAL? 12

F-TEST FOR THE DIFFERENCE BETWEEN TWO VARIANCES 2 2 H0: δ TAKWA = δ RONDO 2 2 H1: δ TAKWA ǂ δ RONDO 13

F value = 1.15 < 2.97823702; Do not reject p-Value = .41470805 > .05; do not reject 14

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.