Respuesta :
Answer:
1. The facts are;
[tex]\overline x _1[/tex] = 95 days
sā = 32 days
nā = 18 SUV's
[tex]\overline x _2[/tex] = 48 days
nā = 38 small cars
sā Ā = 24 days
The confidence level = 95%
The confidence interval is (29.55, Ā 64.45)
Step-by-step explanation:
The facts of the problem are;
The number of SUV's he sold, nā = 18 SUV's
The average number it took to sell the 18 SUV's, [tex]\overline x _1[/tex] = 95 days
The standard deviation of the time it took to sell the 18 SUV's, sā = 32 days
The number of small cars he sold, nā = 38 small cars
The average number it took to sell the 38 small cars, [tex]\overline x _2[/tex] = 48 days
The standard deviation of the time it took to sell the 38 small cars, sā Ā = 24 days
The 95% confidence interval is given as follows;
Using a graphing calculator, we get, the critical-t, [tex]t_c[/tex] = 2.055529
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm t_{c} \cdot\sqrt{\dfrac{s _{1}^{2}}{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}[/tex]
[tex]\left (95-48 \right ) \pm 2.055529 \times \sqrt{\dfrac{32^{2}}{18}+\dfrac{24^{2}}{38}}[/tex]
We get C.I. = 29.55259 < Ī¼ā - Ī¼ā < 64.44741
ā“ C.I. ā 29.55 < Ī¼ā - Ī¼ā < 64.45
