91Ó°ÊÓ

Given In the question that Two means $z$tests and two means $z$interval Procedure are used for comparing population mean. we have to calculate the assumption for using two mean $z$test and two mean $z$interval procedure.

he two-means$z$test and the two-means $z$-interval procedure require the presence of two normally distributed but independent populations with known standard deviations ${\mathrm{σ}}_{1}and{\mathrm{σ}}_2$.

The hypotheses test formula is as follows:

$z=\frac{\left({\stackrel{¯}{x}}_1-{\stackrel{¯}{x}}_2\right)-\left({\mathrm{μ}}_1-{\mathrm{μ}}_2\right)}{\sqrt{\frac{{\mathrm{σ}}_1^2}{n_1}+\frac{{\mathrm{σ}}_1^2}{n_1}}}$

Where $\overline{x_1}and\overline{x_2}$are the means of two sample.

${\mathrm{μ}}_1-{\mathrm{μ}}_2$-Hypothesized difference between the population mean.

${\mathrm{σ}}_{1}and{\mathrm{σ}}_2$-Standard deviation

$n_{1}and{n}_2$-size of the two samples.

Null hypothesis: $H_0:{\mathrm{μ}}_1={\mathrm{μ}}_{2}OR{H}_0:{\mathrm{μ}}_1-{\mathrm{μ}}_2=0$

Alternate hypothesis : $H_0:{\mathrm{μ}}_1≠{\mathrm{μ}}_{2}OR{H}_0:{\mathrm{μ}}_1-{\mathrm{μ}}_2≠0$

This method is works only if standard deviation ${\mathrm{σ}}_{1}and{\mathrm{σ}}_2$are known.