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Chapter 7: Q6 (page 340)

In Exercises 5–8, use the given information to find the number of degrees of freedom, the critical values χL2andχR2, and the confidence interval estimate of σ. 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.

Weights of Pennies 95% confidence;n= 37,s= 0.01648 g.

Short Answer

Expert verified

The degrees of freedom is 36.

The critical values areχL2=21.3359 andχR2=54.4373.

The 95% confidence interval estimate of σis 0.013 g <σ<0.021 g.

Step by step solution

01

Given information

The size of the sample is n=37.

The sample standard deviation is s=0.01648g.

The level of confidence is 95%.

02

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

The degrees of freedom is computed as,

df=n-1=37-1=36

Using the Chi-square table, the critical values are χL2=21.3359andχR2=54.4373.

The 95% confidence interval estimate of σis computed as,

n-1s2χR2<σ<n-1s2χL237-10.01648254.4373<σ<37-10.01648221.33590.013<σ<0.021

Therefore, the 95% confidence interval estimate of role="math" localid="1648104834948" σ isrole="math" localid="1648104851448" 0.013g<σ<0.021g

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