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Chapter 7: Q6 (page 340)

In Exercises 5鈥�8, use the given information to find the number of degrees of freedom, the critical values 蠂L2and蠂R2, 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.

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

Short Answer

Expert verified

The degrees of freedom is 36.

The critical values are蠂L2=21.3359 and蠂R2=54.4373.

The 95% confidence interval estimate of 蟽is 0.013 g <蟽<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 蠂L2=21.3359and蠂R2=54.4373.

The 95% confidence interval estimate of 蟽is computed as,

n-1s2蠂R2<蟽<n-1s2蠂L237-10.01648254.4373<蟽<37-10.01648221.33590.013<蟽<0.021

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

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