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

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Answered 1 year ago
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For part a):

The confidence interval for the difference between two populations means μ1μ2\mu_1-\mu_2 when samples are large enough (30)(\ge30) and drawn from two populations with unknown and unequal standard deviations is given by

(xˉ1xˉ2)±tsxˉ1xˉ2(\bar{x}_1-\bar{x}_2)\pm ts_{\bar{x}_1-\bar{x}_2}

where xˉ1\bar{x}_1 and xˉ2\bar{x}_2 are the means of the two samples, sxˉ1xˉ2s_{\bar{x}_1-\bar{x}_2} is the estimator of standard deviation of xˉ1xˉ2\bar{x}_1-\bar{x}_2, and tt is found from the tt distribution table for the given confidence level and calculated degrees of freedom.

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