231k views
0 votes
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.

1 Answer

5 votes

Answer:

Chi-Square value for lower bond: X²
_(27;0.99)= 46963

Chi-Square value for upper bond: X²
_(27;0,01)= 12.878

Confidence interval: [0.0278;0.1001]

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
_(n-1)

σ²

The formula for the interval is:

Lower bond:

(n-1)S² = 27*0.0484 = 1.3068 = 0.0278


_(n-1;1-α/2)
_(27;0.99) 46.963

Upper bond:

(n-1)S² = 2*0.0484 = 1.3068 = 0.1001


_(n-1;α/2)
_(27;0,01) 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!

User Varis Darasirikul
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories