Respuesta :
Answer:
a)0.654
b)-0.34
Step-by-step explanation:
a)2 3 4 5 6 7
[tex]\mu = 4[/tex]
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{2+3+4+5+6+7}{6}\\Mean =4.5[/tex]
Standard deviation [tex]=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]
Standard deviation [tex]=\sqrt{\frac{(2-4.5)^2+(3-4.5)^2+(4-4.5)^2+(5-4.5)^2+(6-4.5)^2+(7-4.5)^2}{6-1}}=1.87[/tex]
[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\t=\frac{4.5-4}{\frac{1.87}{\sqrt{6}}}\\t=0.654[/tex]
Df = n-1 = 6-1 = 5
Assume α=0.05
So[tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]
So, t critical = 2.57
So, t calculated < t critical
b)1 2 2 5 5 7
[tex]\mu = 4 \\Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{1+2+2+5+5+7}{6}\\Mean =3.67[/tex]
Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]
Standard deviation =[tex]\sqrt{\frac{(1-3.67)^2+(2-3.67)^2+(2-3.67)^2+(5-3.67)^2+(5-3.67)^2+(7-3.67)^2}{6-1}}=2.338[/tex]
[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}t=\frac{3.67-4}{\frac{2.338}{\sqrt{6}}}t=-0.34[/tex]
Df = n-1 = 6-1 = 5
Assume α=0.05
So, [tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]
So, t critical = 2.57
So, t calculated < t critical
