Page 65 - Basic Statistics

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To test the above hypothesis using approach the normal distribution, the

Z value is calculated as follows:
2
2
a. If both population variance ( 1 and 2 ) is known, then

X X −
Z = 1 2 ( N2 )
σ
X 1 − X 2

and

σ 2 σ 2
σ = 1 + 2 ( N3 )
X 1 − X 2 n 1 n 2

Where,

σ = Population standard deviation of difference between two means
X 1 − X 2
1 = Variance of the first population
2
2 = Variance of the second population
2
n1 = Number of observations in the first sample
n2 = Number of observations in the second sample

b. If both the population variance is unknown but n1  30 and n2  30, then

X X −
Z = 1 2 ( N4 )
σ ˆ
X 1 − X 2

and

σ ˆ 2 σ ˆ 2
σ ˆ = 1 + 2 ( N5 )
X 1 − X 2 n 1 n 2

Where,

σ ˆ = Estimated value for the population standard deviation of difference
X 1 − X 2

between two means

2
σ ˆ = Estimated value for the first population variance
1

~~* CHAPTER 4 TESTING HYPOTHESIS *~~