“TWO SAMPLE MEAN”TWO SAMPLE MEAN”PAIRED T-TESTPAIRED T-TEST

SUNDUS TOOR SUNDUS TOOR

PAIRED t-TEST:PAIRED t-TEST:

“Paired t-test is a statistical technique

that is used to compare two population

means“

DistributionDistribution of the Paired of the Paired t-Statistict-Statistic

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Suppose x is a variable on each of two populations whose members can be paired. Further suppose that the paired-difference variable d is normally distributed. Then, for paired samples of size n, the variable

has the t-distribution with df = n – 1.

The normal null hypothesis is that μD = 0

1;/

nvnDs

Ddt

Steps for paired t-testSteps for paired t-test::4

Step 1: The null hypothesis is H0: D = 0; the alternative hypothesis is one of the following:

Ha: D 0 Ha: D < 0 Ha: D > 0

(Two Tailed) (Left Tailed)(Right Tailed)Step 2: Decide on the significance level,

Step 3: The critical values are :±t/2 -t +t

(Two Tailed) (Left Tailed) (Right Tailed)

with df (degree of freedom)= (n – 1).

Region analysis for paired Region analysis for paired t-test :t-test :

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Step 4 : Compute the value of the test statistic

Step 5: If the value of the test statistic falls in the rejection region, reject H0, otherwise do not reject H0.

0normally where/

D

nDsDd

t

EXAMPLEEXAMPLE:

SolutionSolution:

Conclusion:Conclusion:

Comparison b/w 2 means. Comparing changes Estimating the designs

“THANKYOU”THANKYOU”