Question

Show that if the two independent samples of size n? and n? are drawn at random from two normal populations with means ?? & ?? and variances ??² & ??² , respectively, then the sampling distribution of the differences of means, ?? – ?? , is normally distributed with mean and variance given by ?_{??-??} = ?? – ?? and ?²_{??-??} = ??²/n? + ??²/n? .

Name: Show that if the two independent samples of size n? and n? are drawn at random from two normal populations with means ?? ?? and variances ??² ??² , respectively, then the sampling distribution of the differences of means, ?? – ?? , is normally distributed with mean and variance given by ???-?? = ?? – ?? and ?²??-?? = ??²/n? + ??²/n? .
Uploaded: 2023-08-06T23:48:14-08:00
Duration: 2 min 52 s
Channel: Sheryl Ezze
Description: Show that if the two independent samples of size n? and n? are drawn at random from two normal populations with means ?? ?? and variances ??² ??² , respectively, then the sampling distribution of the differences of means, ?? – ?? , is normally distributed with mean and variance given by ???-?? = ?? – ?? and ?²??-?? = ??²/n? + ??²/n? .

          Show that if the two independent samples of size n? and n? are drawn at random from two normal populations with means ?? & ?? and variances ??² & ??² , respectively, then the sampling distribution of the differences of means, ?? – ?? , is normally distributed with mean and variance given by ?_{??-??} = ?? – ?? and ?²_{??-??} = ??²/n? + ??²/n? .

Show that if the two independent samples of size n? and n? are drawn at random from two normal populations with means ?? ?? and variances ??² ??² , respectively, then the sampling distribution of the differences of means, ?? – ?? , is normally distributed with mean and variance given by ???-?? = ?? – ?? and ?²??-?? = ??²/n? + ??²/n? .

Added by Kayla L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

08/06/2023

Step 1

The CLT states that the sampling distribution of the sample mean of a sufficiently large sample from a population with any shape distribution will be approximately normally distributed, provided the population's standard deviation is finite. This theorem applies Show more…

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Show that if the two independent samples of size n1 and n2 are drawn at random from two normal populations with means μ1 and μ2 and variances σ1^2 and σ2^2, respectively, then the sampling distribution of the differences of means, X1 - X2, is normally distributed with mean μ1 - μ2 and variance σ1^2/n1 + σ2^2/n2.