Sam is planning to invest in plantation stock market. His friend recommended thr
ID: 3156022 • Letter: S
Question
Sam is planning to invest in plantation stock market. His friend recommended three plantations stock. Sam collects random samples of monthly returns of each plantation stock and analysis them as in the following table.
(a) Construct a 95% confidence interval of the population standard deviation of each plantation
(b) Rank the plantation stocks from less risk to the most risky investment based on the result in (a)
Plantation Number of Samples Sample Standard deviation THB Plantation 40 7.29 Silver Hope Plantation 46 8.06 PLP Plantation 39 7.52Explanation / Answer
a) For THB plantation, n=40, df=n-1-39,s=7.29, for 95% c.i, alpha=0.05, which gives 2.5% area in each end of Chi-square distribution, therefore, X^20.975=58.1201 and X^20.025=23.6453
95% Interval is:sqrt (n-1)s^2/X^20.025 <= sigma<= (n-1)s^2/X^20.975
=(40-1)*7.29^2/23.6453<=sigma<=(40-1)*7.29^2/58.1201
=5.98<=sigma<=9.36
b) For Silver Hope plantation,
95% Interval is:sqrt (n-1)s^2/X^20.025 <= sigma<= (n-1)s^2/X^20.975
=(46-1)*8.06^2/28.3662<=sigma<=(46-1)*8.06^2/65.4102
=6.69 <=sigma<=10.15
c) For PLP plantation,
95% Interval is:sqrt (n-1)s^2/X^20.025 <= sigma<= (n-1)s^2/X^20.975
=(39-1)*7.52^2/23.6543<=sigma<=(39-1)*7.52^2/58.1201
= 6.08<=sigma<=9.53
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