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Chapter 7: Q5 (page 339)

In Exercises 5鈥�8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2R, and the confidence interval estimate of 蟽. The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in Menthol Cigarettes 95% confidence;n= 25,s= 0.24 mg.

Short Answer

Expert verified

The degrees of freedom is 24.

The critical values are 蠂L2=12.401 and 蠂R2=39.364.

The 95% confidence interval estimate of is 0.19mg<蟽<0.33mg.

Step by step solution

01

Given information

The size of the sample is n=25.

The sample standard deviation is s=0.24.

The level of confidence is 95%.

02

Compute the degrees of freedom, critical values and confidence interval estimate of σ

The degrees of freedom (df) is computed as,

df=n-1=25-1=24

Using the Chi-square table, the critical values are 蠂L2=12.401and 蠂R2=39.364.

The 95% confidence interval estimate of is computed as,

role="math" localid="1648052944759" n-1s2蠂R2<蟽<n-1s2蠂L225-10.24239.364<蟽<25-10.24212.4010.19<蟽<0.33

Therefore, the 95% confidence interval estimate of role="math" localid="1648052981275" 蟽isrole="math" localid="1648052969717" 0.19mg<蟽<0.33mg.

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