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Large sample test _Sample size

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					Z Formula

Abhay chawla

Large sample test (Sample size > 30)
– One sample mean problem

• • • •

The null hypothesis is H0 :  = a . The alternate hypothesis is any one of the following Ha :  > a or Ha :  < a or Ha :   a The Test statistic is

• Z is a std normal variable. If σ is unknown use the sample SD ‘s’. Let the calculated value of Z is , say, c. • If p = Prob(Z ≥ c) < 0.05, then we reject the null hypothesis and accept the alternate one. That means the observed difference between population mean and sample mean is not due to chance but due to some real effect. • If p ≥ 0.05, we accept the null hypothesis and reject the alternate one. i.e. the observed difference between population mean and sample mean is due to chance only.

Two sample mean problem
• The null hypothesis is H0 : 1 = 2 • The alternate hypothesis is any one of the following • Ha : 1 > 2 or Ha : 1 < 2 or Ha : 1  2 • The test statistic is

• Z is a std normal variable. If σ1 and σ2 are unknown, use sample standard deviations s1 and s2.

One sample proportion problem
• The null hypothesis is Ho : P = a . • The alternate hypothesis is any one of the following • Ha : P > a or Ha : P < a or Ha : P  a

• The Test statistic is • Z = p – P where p is the sample √ (PQ/n) proportion, Q = 1 – P and n is the sample size. • Z is a std normal variable.

Two sample proportion problem
• The null hypothesis is H0 : P1 = P2 • The alternate hypothesis is any one of the following • Ha : P1 > P2or Ha : P1 < P2or Ha : P1  P2

• The Test statistic is • Z = p1 – p2 where p1 and p2 are √{PQ (1/n1 + 1/n2)} sample proportions and P = n1p1 + n2p2 n1 + n2 • Q = 1 – P. n1 and n2 are sample size’s. Z is a std normal variable.

Small Sample Test (Sample Size < 30)
• Small Sample Test (Sample Size < 30) • The null hypothesis is H0 :  = a . • The alternate hypothesis is any one of the following • Ha :  > a or Ha :  < a or Ha :   a • The Test statistic is

Small sample test
• One sample mean problem • t = X - µ/s/√n

• t is a Student’s t variable with n – 1 Degrees of freedom.

Two sample mean problem (If any of n1 or n2 less than 30)
• The null hypothesis is H0 : 1 = 2 • The alternate hypothesis is any one of the following • Ha : 1 > 2 or Ha : 1 < 2 or Ha : 1  2 • The test statistic is

• s1 and s2 are sample standard deviations, n1 & n2 sample sizes. • t is a Student’s t variable with n1 + n2 – 2 Degrees of freedom.


				
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posted:7/24/2009
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