Use the given information find the number of degrees of freedom, the critical va

Question

Use the given information find the number of degrees of freedom, the critical values x^2_L and x^2_R, and the confidence interval estimate of c. It is reasonable to assume that a simple has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 80% confidence n = 21, lessthanorequalto = 0.26 mg. (Type a whole number.) x^2_L = (Round no twee decimal places as needed.) x^2_L = (Round to three decimal places as needed.) The confidence interval estimate of n is mg

Explanation / Answer

df=n-1=21-1=20

cal alpha

alpha=1-80%=1-0.8=0.2

find low end confidence interval value

alpha L =alpha lowend=alpha/2=0.2/2=0.1

chi sq 0.1= 28.412

calculate low end confidence interval total

low end=sqrt(n-1)s^2/chi sq alpha/2

=sqrt(20*0.0676/28.412)

=0.2181

To find high end confidence interval value

alpha R

=1-alpha/2=1-0.2/2=1-0.1=0.9

Chi sq (0.9,20) is 12.4426

Calculate high end confidence interval

sqrt(n-1)s^2/chi sq (1-alpha/2)

=sqrt(21-1*0.0676/12.4426

=0.3296

Chi sqL=28.412

chi sq R=12.443

0.22< sigma<0.33

we are 80% confident that the true population std dev lies in between

0.22 and 0.33

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