STA2601 Assignment 3 Solutions 2026

STA2601 Assignment 3 Solutions 2026
UNISA
Unique number: 1352222
Due date: 25 June 2026

, Question 1

Test whether the distribution is symmetric at α = 0.10.

State the hypotheses

𝐻0 : Distribution is symmetric
𝐻1 : Distribution is not symmetric


For a symmetric distribution, the population skewness is zero.

Calculate the sample skewness

Given:

𝑛 = 40
∑(𝑋𝑖 − 𝑋ˉ)2 250.975
𝑚2 = = = 6.274375
𝑛 40
∑(𝑋𝑖 − 𝑋ˉ)3 17.82375
𝑚3 = = = 0.445594
𝑛 40


Sample skewness:
𝑚3
𝑔1 = 3/2
𝑚2
0.445594
𝑔1 = = 0.02835
(6.274375)3/2


Standard error of skewness

6𝑛(𝑛 − 1)
𝑆𝐸(𝑔1 ) = √
(𝑛 − 2)(𝑛 + 1)(𝑛 + 3)

6(40)(39)
=√
(38)(41)(43)
= 0.37378
Test statistic
𝑔1
𝑍=
𝑆𝐸(𝑔1 )
0.02835
=
0.37378
= 0.076