Question :
A random sample of size n1 = 25, taken from a normal population with a
standard deviation σ1 = 5, has a mean1 = 80.A second random sample of size n2 = 36, taken from a different normal
population with a standard deviation σ2 = 3, has a mean2 = 75.Find a 94% confidence interval for μ1 – μ2.
Ans : 2.9 < μ1 - μ2 < 7.1
I tried this :
Where does the wrong come?
Thank you for your help.
Best Answer
Hint: Let random variables $\bar{X}$ and $\bar{Y}$ be sample means from random samples drawn from our two distributions. Let $W=\bar{X}-\bar{Y}$. Then $W$ has mean $\mu_1-\mu_2$. So it is an unbiased estimator of $\mu_1-\mu_2$.
The random variable $W$ has normal distribution. The variance of $W$ is $\frac{25}{25}+\frac{9}{36}$.