Here's the formula for $t-$value for the Unequal variance $t-$test for two independent samples.

$t=\frac{{\stackrel{}{x}}_1-{\stackrel{}{x}}_2}{\sqrt[\phantom{2}]{\frac{s_1^2}{N_1}+\frac{s_2^2}{N_2}}}$

where

$x1$ bar is the mean of sample $1$

X$2$bar is the mean of sample $2,$

s$1$ is the standard deviation of sample $1$

s$2$ is the standard deviation of sample $2$

$N1$ is the sample size of sample $1$

$N2$ is the sample size of sample $2$

Now assume the following to answer the questions below

Sample $1$ is the life satisfaction scores by OLDER adults

Sample $2$ is the life satisfaction scores by YOUNGER adult

$1)$

What is X$1$bar $($the first character on the nominator$)-$the mean for life satisfaction scores by OLDER adults?

A$)42$

B$)43$

C$)43\mathrm{.}5$

D$)44$

E$)44\mathrm{.}5$

F$)45$

What is X$2$bar$-$the mean for life satisfaction scores by YOUNGER adults?

A$)26\mathrm{.}2$

B$)26\mathrm{.}6$

C$)27\mathrm{.}4$

D$)28\mathrm{.}1$

E$)29\mathrm{.}6$

What is s$1-$the standard deviation of the distribution$-$of life satisfaction scores by OLDER adults?

A$)8\mathrm{.}21$

B$)7\mathrm{.}67$

C$)7\mathrm{.}40$

D$)8\mathrm{.}68$

E$)8\mathrm{.}97$

What is s$2-$the standard$-$deviation of the distribution$-$of life satisfaction scores by YOUNGER adults?

A$)8\mathrm{.}54$

B$)8\mathrm{.}76$

C$)7\mathrm{.}48$

D$)6\mathrm{.}48$

E$)9\mathrm{.}11$

What is N$1-$the sample size of the OLDER adults and N$2-$the sample size of the YOUNGER adults.

A$)8$ and $10$

B$)10$ and $10$

C$)12$ and $10$

D$)10$ and $12$

E$)20$ and $10$

If the question being asked by the researcher was:is the life satisfaction greater among older adults compared with younger adults, what kind of t$-$test would be used?

A$)$old tailed t$-$test

B$)$two tailed t$-$test

If the wuestion being asked by the researcher was : is the life satisfaction diffrent for older adults compared to younger adults, what kind of t$-$test would be used?

A$)$one tailed t$-$test

B$)$two tailed t$-$test