91Ó°ÊÓ

Using the critical value strategy or the $p$value approach, determine the required hypothesis.

The hypothesis test to be carried out is as follows:

$H_{\mathrm{a}}:{\mathrm{μ}}_1<{\mathrm{μ}}_2$

The test is run at a significance level of $\mathrm{Î\pm }=0.05$which is equal to $5\%$.

The test statistic's value is calculated as follows:

The value of test statistic is calculated as,

$t=\frac{{\stackrel{¯}{x}}_1-{\stackrel{¯}{x}}_2}{\sqrt{\left(\frac{s_1^2}{n_1}\right)+\left(\frac{s_2^2}{n_1}\right)}}$

$=\frac{7.36-10.50}{\sqrt{\left(\frac{1.{22}^2}{14}\right)+\left(\frac{4.{59}^2}{6}\right)}}$

$=-1.65$

The$t$statistic has $df=\mathrm{Δ}$

The probability of seeing a value$t=-1.65$is given by the localid="1651290852925" $P$value.

The value of localid="1651290856971" $P$obtained using technological means is localid="1651290861835" $0.0798$.

The significance level of localid="1651290866001" $1\%$is exceeded by the localid="1651290870640" $P$value.

As a result, at the localid="1651290901161" $5\%$level, the results are not statistically significant.