Hypothesis Testing:z-test

Ravi trivedi

Roll No -10101096

TEST OF HYPOTHESIS FOR SAMPLES -------------------

•Test Of Hypothesis about population mean •Test Of Hypothesis about difference between two population means•Test Of Hypothesis about difference between two population S.D’S.•Test Of Hypothesis about population proportion.•Test Of Hypothesis about difference between two population proportion.

•Test Of Hypothesis about population mean ---

The test of hypothesis concerning population mean in case of large sample requires the use of normal distribution . let be the mean of a large random sample of size n drawn from a normal population with mean & Standard deviation σ . Null hypothesis: H0: μ1 = μ2 or H0: μ1 – μ2 = 0 alternative hypothesis: Ha: μ1 − μ2 or: Ha: μ1 − μ2 ≠ 0

n

Xz 121

1||

[2] Test Of Hypothesis about difference between two population means ------------

LET X1 & X2 THE SAMPLE MEANS OF INDEPENDENT RANDOM SAMPLES OF LARGE SIZES N1 & N2 DRAWN FROM TWO POPULATIONS HAVINGMEANS µ 1 & µ 2 & STANDARD DEVIATIONS 1 & 2 . TO TEST WHETHER THE TWO POPULATION MEANS ARE OR NOT , THE APPROPRIATE TEST STATISTIC TO BE USED IS :

2

22

1

21

2121

nn

XXz

(3)Test Of Hypothesis about difference between two population s.d’s.---------------

Let s1 & s2 be the standard deviation of two independent random samples of sizes n1 & n2 from two populations with standard deviations 1 & 2 respectively . to test whether the two populations S.D.’S are equal or not , one appropriate test statistic is to be used as . (S1 –S2 )- (1 - 2)Z = ---------------------------------------- S.E.S1 -S2 S1 =S.D. OF the 1st sample , s2 = s.d. of the 2nd sample , SES1_S2 = Standard error of the difference between two s.d.’s.

•Test Of Hypothesis about population proportion.

A Random sample of size n ( n ≥ 30) has a sample proportion p of members possessing a certain attribute . to test the hypothesis that the population proportion p has a specified value , the appropriate test statistic to be used as :

(5)Test Of Hypothesis about difference between two population proportion.

LET P1 & p2 bethe sample proportions obtained in large sample of sizes n1 & n2 drawn from respective populations having proportions p1 & p2 test the hypothesis that is no difference between the populations , the appropriate test statistic to be used is :  

(p1 – p2 ) - ( p1 – p2 ) Z = ______________________ S.E.p1-p2

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