# File

```TA Section 4, ECN102 2015 Spring
Ilhyun Cho∗
April 22, 2015
Central Limit Theorem
Let X = 1 if the toss of a six-sided die yields a five or six, and let X = 0 otherwise. Then P r[X = 1] =
and P r[X = 0] = 23
1
3
• Obtain µ = E[X] from first principles.
µ = E[X] =
2
1
1
∗ 0 + ∗ 1 = ≈ 0.3333
3
3
3
• Obtain σ 2 = E[(X − µ)2 ] from first principles.
σ 2 = E[(X − µ)2 ] =
2 1 1 4
2
∗ + ∗ = ≈ 0.2222
3 9 3 9
9
Suppose for X ∼ (µ, σ 2 ) like above, we form 10,000 samples of size 100 and obtain 10,000 sample means.
• What approximately do you expect the average of the x
¯ to equal? 0.3333
• What approximately do you expect the variance of the x
¯ to equal? 0.0022
• What approximately do you expect the standared deviation of the x
¯ to equal? 0.0471
Statistical Inference
Suppose Keita argues that the average UC Davis students’ housing rental fee is \$450 per month. Ilhyun
wants to check whether his argument is true or not. Ilhyun surveyed 100 students’ housing rental fee per
month randomly in 2014 spring quarter. The sample mean is \$500 and sample standard deviation is \$250.
Can you reject the null hypothesis at the five-percent level of significance?
H0 : The average students’ housing rental fee is \$450.
H1 : The average students’ housing rental fee is not \$450.
t=
x
¯−µ
√s
n
∼ T (n − 1)
Under H0 ,
t=
500−450
√250
100
=2
Test statistic = |2| > 1.984217 = critical value. Thus, reject H0
dis invttail(99, 0.025) = 1.984217
∗
[email protected], office hours: Wednesday 9:00 am - 11:00 am , 115 SSH.
1
```