$25$ A student researcher developed a novel analytical method for determining the lead $(P{b}^{2+})$ content in waste water. To demonstrate the efficacy of the new method, the researcher measured the $P{b}^{2+}$ concentration in an unknown sample using the novel method $($Method $1).$ She then measured the same sample using the standard, conventional analytical method $($Method $2).$ The results of this experiment are shown as the mean $(\stackrel{}{x})$ and standard deviation $(s)$ of the $P{b}^{2+}$ concentration in parts per million $($ppm$).$ The number of replicate measurements $(n)$ is also given.

Method $1$: $,{\stackrel{}{x}}_1=4\mathrm{.}660ppm,s_1=0\mathrm{.}220ppm,n_1=6$

Method $2$: $,{\stackrel{}{x}}_2=4\mathrm{.}810ppm,s_2=0\mathrm{.}170ppm,n_2=6$

Calculate the $F$ value.

$F_{\text{c}\text{a}\text{l}\text{c}}$

Are the standard deviations significantly different from each other at the $95\%$ confidence level? The value of $F_{\text{t}\text{a}\text{b}\text{l}\text{e}}$ can be found in the table of critical $F$ values.

yes

no

Calculate the value of $t_{\text{c}\text{a}\text{l}\text{e}}$ to compare the data sets from Method $1$ and Method $2.$

$t_{\text{c}\text{a}\text{l}\text{c}}=$