Use the given information to find the number of degrees of freedom, the critical values chi Subscript Upper L Superscript 2 and chi Subscript Upper R Superscript 2, and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 98% confidence; nequals28, sequals0.22 mg.

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cchilabert cchilabert · Answer 1 · 2019-12-06T20:02:49+01:00

Answer:

Chi-Square value for lower bond: X²[tex]_{27;0.99}[/tex]= 46963

Chi-Square value for upper bond: X²[tex]_{27;0,01}[/tex]= 12.878

Confidence interval: [0.0278;0.1001]

Step-by-step explanation:

Hello!

You need to make a 98% Confidence interval for the population variance of a single sample. To construct it you have to use a Chi-Square statistic:

X²= (n-1)S² ~X²[tex]_{n-1}[/tex]

σ²

The formula for the interval is:

Lower bond:

(n-1)S² = 27*0.0484 = 1.3068 = 0.0278

X²[tex]_{n-1;1-α/2}[/tex] X²[tex]_{27;0.99}[/tex] 46.963

Upper bond:

(n-1)S² = 2*0.0484 = 1.3068 = 0.1001

X²[tex]_{n-1;α/2}[/tex] X²[tex]_{27;0,01}[/tex] 12.878

n=28

S= 0.22

S²=0.0484

With a 98% confidence level, you'd expect the true value of the nicotine variance in menthol cigarettes is contained by the interval [0.0278;0.1001]

I hope it helps!