Drawn from the same population; sample size>30; Population Std is not known

Find combined mean and combined standard deviation of samples

Formulae used

Then find Z calculated value using

We use combined standard deviation of the samples. For this you have to find Combined means of sample 1 and sample 2. Difference d1 = Xbar1 – Xbar12, d2 = Xbar2- Xbar12. Finally find

Find combined mean

Find combined Standard deviation:

Find Z-calculated value

Conclusion

Abs(z) 0.191969 is less than abs(z critical value)1.96  we accept Null Hypothesis as we do not have any evidence to reject as difference is not statistically significant

Using Python:

 

Find combined average/mean of A and B

Find combined sigma of A and B and Z calculated value

Find z critical value 

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Find Z calculated value using function

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