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Chapter 7: Q7 (page 340)

In Exercises 5–8, 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 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.

Platelet Counts of Women 99% confidence;n= 147,s= 65.4.

Short Answer

Expert verified

The degrees of freedom is 146.

The critical values are χL2=105.7411 and χR2=193.7611.

The 99% confidence interval estimate is 56.8<σ<76.8.

Step by step solution

01

Given information

The size of the sample is n=147.

The sample standard deviation is s=65.4.

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=147-1=146

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 146 degrees of freedom are χL2=105.7411and χR2=193.7611.

The 95% confidence interval estimate of is computed as,

n-1s2χR2<σ<n-1s2χL2147-165.42193.7611<σ<147-165.42105.741156.8<σ<76.8

Therefore, the 99% confidence interval estimate of σis 56.8<σ<76.8.

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