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Chapter 11: Q.108 (page 668)

If df=2, the chi-square distribution has a shape that reminds us of the exponential.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Given information

Given in the question that, we have to find that whether the statement is true or false

02

Explanation

The gamma distribution with shape parameter n2and scale parameter 1can be written as shown below:

f(x)=12n2Γn2xn2−1e−x2

The chi-square distribution with2 degrees of freedom can be written as a gamma distribution with the shape parameter as one and the scale parameter as one. And it is understood that this is the exponential distribution with scale parameter 2. Therefore, the statement is true.

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Most popular questions from this chapter

An ice cream maker performs a nationwide survey about favorite flavors of ice cream in different geographic areas of the U.S. Based on the Table, do the numbers suggest that geographic location is independent of favorite ice cream flavors? Test at the 5%significance level.

USRegionStraChocoVanRockyRoadMintChocolateChipPistachioTotalWest1221221915897Midwest1032221115696East83127815796South1528308156102Total45112101466027391

State the null and alternative hypotheses?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is six with a variance of nine at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief.

Where is μlocated on a chi-square curve?

In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.
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