Unemployment rate

Over the last 16 years, the country's unemployment rate has changed according to the following frequency table:
years of unemployment: 2 5 2 3 3 1
unemployment rate: 0.5 1 1.5 2 2.5 3 in % (percent).

Determine the two-sided confidence interval for the variance DN with a confidence level of 0.95.

Correct answer:

a =  1.224 %
b =  1.9635 %

Step-by-step explanation:

n=2+5+2+3+3+1=16 α=0.95  μ=2 0.5+5 1+2 1.5+3 2+3 2.5+1 3n=2 0.5+5 1+2 1.5+3 2+3 2.5+1 316=51321.5938  E2=2 (0.5μ)2+5 (1μ)2+2 (1.5μ)2+3 (2μ)2+3 (2.5μ)2+1 (3μ)2=2 (0.51.5938)2+5 (11.5938)2+2 (1.51.5938)2+3 (21.5938)2+3 (2.51.5938)2+1 (31.5938)2=583649.1094  V=E2/n=9.1094/16=58310240.5693  σ=V=0.56930.7545 α=0.95 α2=1(10.95)/2=3940=0.975 u(0.975)=1.96 u=1.96  r=u σ/n=1.96 0.7545/160.3697  a=μr=1.59380.3697=1.224%

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