Please solve both questions$($ handwritten $)$ step by step $.$ I have

final answer but I need step by step for my study. I will rate

answer. Thank you

Question $1(2$ marks$)$

The information below is based on independent random samples taken from two normally distributed populations having

equal variances. Based on the sample information, determine the $95\%$ confidence interval estimate for the difference between the

two population means.

$n_1=60,{\stackrel{}{x}}_1=409,{}_1=15$

$n_2=39,{\stackrel{}{x}}_2=367,{}_2=27$

Question $2(3$marks$)$

A decision$-$maker wishes to test the null and alternative hypotheses shown below using an alpha level equal to $0\mathrm{.}05.$ The

population standard deviations are assumed to be known. After the sample data are collected, the test statistic is computed to be

$z=1\mathrm{.}98.$ What conclusion should be reached?

$H_0$:${}_1-{}_2=0$

$H_A$:${}_1-{}_{2}0$