Test the claim about the difference between two population means ${}_1$ and ${}_2$ at the level of significance $.$ Assume the samples are random and independent, and the

populations are normally distributed.

Claim: ${}_1={}_2$;$=0\mathrm{.}05.$ Assume ${}_1^2={}_2^2$

Sample statistics: ${\stackrel{}{x}}_1=34\mathrm{.}3,s_1=3\mathrm{.}5,n_1=10$ and

${\stackrel{}{x}}_2=35\mathrm{.}8,s_2=2\mathrm{.}3,n_2=17$

$H_a$:${}_1{}_2^{-}$

$H_a^{-}$:

Find the standardized test statistic t$.$

$t=$

$($Round to two decimal places as needed.$)$

Find the P$-$value.

$P=$

$($Round to three decimal places as needed.$)$

Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

$H_0.$ There

enough evidence at the $5\%$ level of significance to reject the claim.