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Chapter 11: Q.3 (page 652)

When does the chi-square curve approximate a normal distribution?

Short Answer

Expert verified

If df>90because chi square is approximated as a normal curve, this suggests that the distribution is normal.

X~N1000,44.72

Step by step solution

01

Given Information

We have to determine when does the chi-square curve approximate a normal distribution.

02

Explanation

Formulas using here is as follows

μx2=df

σx2=2×df

If df>90because chi square is approximated as a normal curve, this suggests that the distribution is normal.

for X~X21000the population mean will be

μ=dfdf=1000μ=1000

standard deviation will be

σ=2×df=2×1000≈44.72

Therefore we have

X~N1000,44.72approx

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Most popular questions from this chapter

A 2013poll in California surveyed people about taxing sugar-sweetened beverages. The results are presented in the Table and are classified by ethnic group and response type. Are the poll responses independent of the participants’ ethnic group? Conduct a test of independence at the 5%significance level.

OpinionlEthnicityAsian-AmericanWhite/Non-HispanicAfrican-AmericanLatinoRowTotalAgainst tax4843341160682In Favor of tax5423424147459No opinion1643161994Column Total118710813261235

The standard deviation of heights for students in a school is 0.81. A random sample of 50students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81.

To find the value ofdf.

Decide whether the following statements are true or false:

As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical.

Is the traveler disputing the claim about the average or about the variance?

Letα=0.05

Decision: ________

Conclusion (write out in a complete sentence.): ________
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