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Chapter 7: Q8 (page 340)

Question: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.

Heights of Men 99% confidence;n= 153,s= 7.10 cm.

Short Answer

Expert verified

The degrees of freedom is 152.

The critical values are 蠂L2=110.8458 and 蠂R2=200.6568.

The 99% confidence interval estimate is 56.9<蟽 <76.6.

Step by step solution

01

Given information

The size of the sample is n=153.

The sample standard deviation is s=7.10.

The level of confidence is 99%.

02

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

The degrees of freedom is computed as,

df=n-1=153-1=152

The level of confidence is 99%, which implies that the level of significance is 0.01.

Using the Chi-square table, the critical values at 0.01 level of significance and at 152 degrees of freedom are 蠂L2=110.8458 and蠂R2=200.6568.

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

n-1s2蠂R2<蟽<n-1s2蠂L2153-165.42200.6568<蟽<153-165.42110.845856.9<蟽<76.6

Therefore, the 99% confidence interval estimate of role="math" localid="1648107586512" 蟽 is role="math" localid="1648107574037" 56.9<蟽<76.6.

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