Question

Discuss the basic strategy for comparing the means of two populations based on a simple random paired sample.

Short answer

The following advancements outline the basic technique for examining the methods for two populations of paired sample based on free basic irregular examples:

1. Select an example from the matched sample independently and arbitrarily.

2. Analyze the difference between the matched values of the variable under investigation.

3. Remove an unneeded source of variance with a paired sample.

4. As a result of the checking blunder made in assessing the impact between the populaces means, the effect between the populaces means will typically be less and, in this manner, obligated to differentiate distinction between the people indicates when such references exist.

Step-by-step solution

Given Information

To go through the basics of using an independent simple random paired sample to compare the means of two populations.

Explanation

Assume that for the paired sample, $x$is a regularly distributed variable.

The difference between the values of the variable $X$on the members of the pair designated by $d$is called the paired difference variable and is calculated for each pair.

${\mu }_d={\mu }_1-{\mu }_2$

The random variable for the paired sample is normally distributed.

Test statistics:

When the population standard deviations are known, compare two population means.

$z=\frac{\left(\overline{x_1}-\overline{x_2}\right)-\left({\mu }_1-{\mu }_2\right)}{\sqrt{{\left(\frac{c_1}{n_1}\right)}^2+{\left(\frac{c_2}{m_2}\right)}^2}}$

In a paired sample of size $n$, compare two population means as follows:

$t=\frac{\overline{d}-{\mu }_d}{\frac{s_d}{\sqrt{n}}}~t_{(n-1)}$

Where $s_d$is the standard deviation