Respuesta :
Solution :
Sample size Sample mean Sample S.D.
Sample 1 [tex]$n_1=36$[/tex] [tex]$\bar{x}_1=150,000$[/tex] [tex]$s_1=17,000$[/tex]
Sample 2 [tex]$n_2=45$[/tex] [tex]$\bar{x}_2=100,000$[/tex] [tex]$s_2=12,000$[/tex]
[tex]$df = \frac{\left(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s_1^2}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s_2^2}{n_2}\right)^2}$[/tex]
= 60
Therefore, significance level, α = 0.1
Critical value, t* = 1.6706
So, the margin of error, [tex]$t^*=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$[/tex]
= 559.9896
Lower limit, [tex]$(\bar x_1-\bar x_2)-\text{(margin of error)}=44402.0104$[/tex]
Upper limit, [tex]$(\bar x_1-\bar x_2)+\text{(margin of error)}=55597.9896$[/tex]
Therefore 90% C.I. is (44402.0104, 55597.9896) or [tex]$44402.0104 < \mu_1 - \mu_2 < 55597.9896$[/tex]
