Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6, 7, 8, and 9.
1. How many samples are possible? List them and compute the mean of each sample.
2. Construct the sampling distribution of the sample means.
3. Construct the histogram of the sampling distribution of the sample means. Describe the shape of the histogram.
Help. Kahit yung number 1 lang ma solve. Thank you in advance
Answers
Answer:
Calculate the standard deviation of the sampling distribution of the sample means . Compare this to the standard deviation of the population.
Step-by-step explanation:
E[\bar X_5^2] =(6.2^2+6.6^2+6.8^2+ 7.0^2+7.2^2+7.4^2+7.8^2+8.0^2+8.6^2+ 8.8^2+9.0^2+9.2^2+9.6^2 +9.8^2+2⋅8.2^2+2⋅8.4^2 +3⋅7.6^2)/21=1362.8/21=64\frac{94}{105}E[
X
ˉ
5
2
]=(6.2
2
+6.6
2
+6.8
2
+7.0
2
+7.2
2
+7.4
2
+7.8
2
+8.0
2
+8.6
2
+8.8
2
+9.0
2
+9.2
2
+9.6
2
+9.8
2
+2⋅8.2
2
+2⋅8.4
2
+3⋅7.6
2
)/21=1362.8/21=64
105
94
Var[\bar X_5 ]=E[\bar X_5^2 ]-E[\bar X_5 ]^2=64\frac{94}{105}-64=\frac{94}{105}Var[
X
ˉ
5
]=E[
X
ˉ
5
2
]−E[
X
ˉ
5
]
2
=64
105
94
−64=
105
94
\sigma(\bar X_5 )=\sqrt{Var[\bar X_5 ]}=\sqrt{94/105}=\sigma(X)/\sqrt{15}=0.946σ(
X
ˉ
5
)=
Var[
X
ˉ
5
]
=
94/105
=σ(X)/
15
=0.946