Sampling

# sampling distribution of difference between means

If two populations follow each normal distributions, N(μ_{1}, σ_{1}) and N(μ_{2}, σ_{2}) (or both of them follow any distribution with these means and SD), and each samples are big enough in size n_{1} and n_{2}, then the **sampling distribution of difference between means** follows a normal distribution

and the standard normal distribution comes by the expression:

Example: an electrical appliance made by Company A has an average life of 2500 hours, with a SD of 500 hours. Another Company, B, makes this appliance with an average life of 2300 hours, and a SD of 800 hours. We take 300 Company A devices and 200 Company B devices. Calculate the probability that the average life of the sample from Company A isn’t 100 hours more than the average life of the sample from Company B.

**Exercise**: The mean height of 15-year-old boys (in cm) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. If eight boys and eight girls were sampled, what is the probability that the mean height of the sample of girls would be higher than the mean height of the sample of boys?

Solution: 0.0062

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