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Chapter 12: Q. 12.8 (page 484)

For a χ2-curve with df=4, determine

a. χ0.0052

b.χ0.012

Short Answer

Expert verified

Part a: The χ2value that has area 0.005with 4degrees of freedom is, 14.86which is illustrated graphically below,

Part b: The χ2value that has area 0.01with 4degrees of freedom is, 13.28which is illustrated graphically below,

Step by step solution

01

Part a Step 1. Given information

The number of degrees of freedom is,4.

02

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

The number of degrees of freedom is, 4.So, first we go outside the columns. Then going across that row to the column labeled χ0.0052, we reach 14.86.

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,4.

05

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

The number of degrees of freedom is, 4.So, first we go outside the column. Then going across that row to the column labeled χ0.012, we reach13.28.

06

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

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Most popular questions from this chapter

Housing Foundations. The U.S. Census Bureau publishes information about housing units in American Housing Survey for the United States. The following table cross-classifies single-unit occupied housing units by foundation type and tenure of occupier. The frequencies are in thousands.

For single-unit occupied housing units:


OwnerRenterTotal
Full-basement22,9873,30126,288
Partial-basement7,5169908,506
Crawl-space14,2893,47717,776
Concrete slab21,0135,65126,664
Other9493341,283
Total66,75413,75380,507

a. How many have crawl spaces?

b. How many are owner occupied?

c. How many are rented and have full basements?

d. How many have a basement?

e. How many are either owner occupied or have a concrete slab?

Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.

a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.

b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal

c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?

d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.

If the observed and expected frequencies for a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test matched perfectly, what would be the value of the test statistic?

The Quinnipiac University Poll conducts nationwide surveys as a public service and of research. This problem is based on the results of once such poll. Independent simple random samples of 300residents each in read (predominantly Republiclian), blue (predominantly Democratic) and purple (mixed) states were asked how satisfied they were with the way things are going today. The following table summarizes the responses.

At the 10%significance level, do the data provide sufficient evidence to conclude that the satisfaction-level distributions differ among residents of red, blue and purple states?

Suppose that bivariate data are to be grouped into a contingency table. Determine the number of cells that the contingency table will have if the numbers of possible values for the two variables are

a. two and three.
b. four and three.
c. m and n.
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