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Chapter 12: Q. 12.5 (page 484)

For a χ2-curve with 19degrees of freedom determine the χ2-value that has area.

a. 0.025to its right

b. 0.01to its right.

Short Answer

Expert verified

Part a: The χ2value that has area 0.025to its right with 19degrees of freedom is 32.85which is illustrated graphically below,

Part b: The χ2value that has area 0.01to its right with 19degrees of freedom which is illustrated graphically,

Step by step solution

01

Part a Step 1. Given information

Degrees of freedom, df=19.

02

Part a Step 2. To find the required χ2 value, we use table V.

The number of degrees of freedom is 19.So we first go down the outside columns . Then going across that row to the column labeled χ0.0252we reach 32.85.

03

Part a Step 3. Let us illustrate our work graphically.

04

Part b Step 1. Given information

The number of degrees of freedom is,19.

05

Part b Step 2. To find the required χ2 value, we use table V.

The number of degrees of freedom is,19. So we first go down the outside columns . Then going across that row to the column labeledχ0.012, we reach36.19.

06

Part b Step 3. Let us illustrate our work graphically.

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Most popular questions from this chapter

Why is the phrase "goodness of fit" used to describe the type of hypothesis test considered in this section?

The chi-square goodness-of-fit test provides a method for performing a hypothesis test about the distribution of a variable that has c possible values. If the number of possible values is 2, that is, c=2, the chi-square goodness-of-fit test is equivalent to a procedure that you studied earlier.

a) Which procedure is that? Explain your answer.

b) Suppose that you want to perform a hypothesis test to decide whether the proportion of a population that has a specified attribute is different from p_0. Discuss the method for performing such a test if you use (1) the one-proportion z-test (page 463) or (2) the chi-square goodness-of-fit test.

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