Respuesta :
Answer:
[tex]0.071,1.928[/tex]
Step-by-step explanation:
Downtown Store North Mall Store
Sample size n 25 20
Sample mean [tex]\bar{x}[/tex] $9 $8
Sample standard deviation s $2 $1
[tex]n_1=25\\n_2=20[/tex]
[tex]\bar{x_1}=9\\ \bar{x_2}=8[/tex]
[tex]s_1=2\\s_2=1[/tex]
[tex]x_1-x_2=9-8=1[/tex]
Standard error of difference of means = [tex]\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}[/tex]
Standard error of difference of means = [tex]\sqrt{\frac{2^2}{25}+\frac{1^2}{20}}[/tex]
Standard error of difference of means = [tex]0.458[/tex]
Degree of freedom = [tex]\frac{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}})^2}{\frac{(\frac{s_1^2}{n_1})^2}{n_1-1}+\frac{(\frac{s_2^2}{n_2})^2}{n_2-1}}[/tex]
Degree of freedom = [tex]\frac{\sqrt{(\frac{2^2}{25}+\frac{1^2}{20}})^2}{\frac{(\frac{2^2}{25})^2}{25-1}+\frac{(\frac{1^2}{20})^2}{20-1}}[/tex]
Degree of freedom =36
So, z value at 95% confidence interval and 36 degree of freedom = 2.0280
Confidence interval = [tex](x_1-x_2)-z \times SE(x_1-x_2),(x_1-x_2)+z \times SE(x_1-x_2)[/tex]
Confidence interval = [tex]1-(2.0280)\times 0.458,1+(2.0280)\times 0.458[/tex]
Confidence interval = [tex]0.071,1.928[/tex]
Hence Option A is true
Confidence interval is [tex]0.071,1.928[/tex]
