ECO 5400: Statistics
Instructor: Bipasha Maity
Ashoka University
Monsoon 2020
Homework Due: Monday, November 23, 2020 by 6 pm via email.
Question 1: Use the table/simulation to find the following critical values:
๐~๐ก Distribution: 1 โ ๐(|๐|โค ๐ก๐๐)= 0.05 for ๐๐ = 5, 10,20,30,50. How
do these compare to the 0.05 critical values of the Normal distribution?
Question 2: Suppose ๐1, ๐2, โฆ. , ๐6 are six random variables that form a random
sample from the standard normal distribution.
Let ๐ = (๐1+ ๐2+ ๐3)2+ (๐4+ ๐5+ ๐6)2
Find the value of ๐ such that the random variable ๐๐ will follow the chi-square
distribution
Question 3: Suppose you are looking at treatment and control group differences to
determine the effectiveness of a computer-skills training programme on weekly
wages. The standard deviation of the weekly wages is $15 for both the treatment
and control groups. Now the average weekly wages for the control group is $100
and $100+ฮด for the treatment group. If you are constrained to have 25% of your
observations in the control group and 75% observations in your treatment group,
how large does ๐ have to be in order for the probability of ๐
๏ค๐โ ๐
๏ค๐ถ> 0 is atleast
95%?
Note: ๐
๏ค๐ and ๐
๏ค๐ถ are the sample averages weekly wages of the treatment and
control groups respectively and ๐ is the total number of observations in your
