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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)=12n2螕n2xn2鈭�1e鈭�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

The Bureau of Labor Statistics gathers data about employment in the United States. A sample is taken to calculate the number of U.S. citizens working in one of several industry sectors over time. Table 11.17 shows the results:

Industry Sector200020102020TotalNonagriculture wage and salary13,24313,04415,01841,305Goods-producing, excluding agriculture2,4571,7711,9506,178Services-providing10,78611,27313,06835,127Agriculture, forestry, fishing, and hunting240214201655Nonagriculture self-employed and unpaid family worker9318949722,797Secondary wage and salary jobs in agriculture and private householdindustries14111136Secondary jobs as a self-employed or unpaid family worker196144152492Total27,86727,35131,37286,590

We want to know if the change in the number of jobs is independent of the change in years. State the null and alternative hypotheses and the degrees of freedom .

The table provides a recent survey of the youngest online entrepreneurs whose net worth is estimated at one million dollars or more. Their ages range from 17to 30. Each cell in the table illustrates the number of entrepreneurs who correspond to the specific age group and their net worth. Are the ages and net worth independent? Perform a test of independence at the 5%significance level.

Age Groupl Net Worth Value (in millions of US dollars)1-56-24鈮�25Row Total17-258752026-3065920Column Total14121440

The expected percentage of the number of pets students have in their homes is distributed (this is the given distribution for the student population of the United States) as in Table 11.12.

Number of PetsPercent0181252303184+9

A random sample of 1,000students from the Eastern United States resulted in the data in Table 11.13.

Number of PetsFrequency02101240232031404+90

At the 1% significance level, does it appear that the distribution 鈥渘umber of pets鈥� of students in the Eastern United States is different from the distribution for the United States student population as a whole? What is the p-value?

Consumers may be interested in whether the cost of a particular calculator varies from store to store. Based on surveying 43 stores, which yielded a sample mean of \(84 and a sample standard deviation of \)12, test the claim that the standard deviation is greater than $15.

The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.
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