Answer:
reject H₀ , {0.8262, 3.1738} at 99% C I
Step-by-step explanation:
[tex]H_0: \mu_1 = \mu_2\\H_1: \mu _1 > \mu _2\\[/tex]
critical value, [tex]\alpha = 0.01[/tex]
degree of freedom: 35 - 1 = 34
critical value: 2.441
from the expression
[tex]t = \frac{(x _1-x_2) - 0}{\sqrt{\frac{\sigma^{2}_x }{n_1} +\frac{\sigma^{2}_x }{n_2} } }[/tex]
[tex]t = \frac{(110-108) - 0}{\sqrt{\frac{1.8^{2} }{35} +\frac{1.8^{2}}{35} } }[/tex]
t = 4.648 > 2.441
H₀ is rejected because t > critical value
(b)
in the second scenario
[tex]I: (x_1 - x_2) +/- t\sqrt{\frac{\sigma^{2}_x }{n_1} +\frac{\sigma^{2}_x }{n_2}[/tex]
1 - 0.99 = 0.01
[tex]\frac{\alpha }{2} = \frac{0.01}{2}= 0.005[/tex]
degree of freedom = 34
t = 2.728
substituting in the above formula
we have
[tex]I: (110 - 108) +/- 2.728\sqrt{\frac{1.80^{2}}{35} +\frac{1.8^{2}}{35}}[/tex]
[tex]I: 2 +/- 1.1738[/tex]
[tex]I:[0.8262, 3.1738][/tex]
we can see the difference of the means is between 0.8262 and 3.1738 at 99% confidence
