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Question

# As mentioned in earlier exercise. Now do that assignment without assuming that the population standard deviations are the same.

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For part a):

The confidence interval for the difference between two populations means $\mu_1-\mu_2$ when samples are large enough $(\ge30)$ and drawn from two populations with unknown and unequal standard deviations is given by

$(\bar{x}_1-\bar{x}_2)\pm ts_{\bar{x}_1-\bar{x}_2}$

where $\bar{x}_1$ and $\bar{x}_2$ are the means of the two samples, $s_{\bar{x}_1-\bar{x}_2}$ is the estimator of standard deviation of $\bar{x}_1-\bar{x}_2$, and $t$ is found from the $t$ distribution table for the given confidence level and calculated degrees of freedom.

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