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Chapter 12: Q. 12.6 (page 484)

For a 蠂2curve with 22degrees of freedom, determine the 蠂2value that has area

a. 0.01to its right.

b. 0.005to its right.

Short Answer

Expert verified

Parta : The 蠂2value that has area0.01to its right with22degrees of freedom is,40.3which is illustrated graphically below,

Partb: The 蠂2value that has area 0.005to its right with 22degrees of freedom is 42.8which is illustrated graphically below,

Step by step solution

01

Part a Step 1. Given information

The number of degrees of freedom is,22.

02

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

The number of degrees of freedom is, 22,so we first go down the outside columns. Then going across that row to the column labeled蠂0.012we reach40.3.

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,22.

05

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

The number of degrees of freedom is,22.so we first go down the outside columns. Then going across that row to the column labeled蠂0.0052we reach42.8.

06

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

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Most popular questions from this chapter

12.51 Farms. The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in


Full ownerPart ownerTenantTotal
Under 50
7044
50-17949213038660
180-499198

368
500-999518414149
1000& over4111417172
Total1521541

a. Fill in the six missing entries.

b. How many cells does this contingency table have?

c. How many farms have under 50 acres?

d. How many farms are tenant operated?

e. How many farms are operated by part owners and have between 500 acres and 999 acres, inclusive?

f. How many farms are not full-owner operated?

g. How many tenant-operated farms have 180 acres or more?

We have presented a contingency table that gives a cross-classification of a random sample of values for two variables x and y, of a population.

Perform the following tasks

a. Find the expected frequencies Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

Girls and Boys. One probability model for child gender is that a boy or a girl is equally likely to be born. If that model is correct, then, for a two-child family, the probabilities are 0.25,0.50, and 0.25 for two girls, one girl and one boy, and two boys, respectively. W. Stansfield and M. Carlton examined data collected in the National Health Interview Study on two-child families in the article "The Most Widely Published Gender Problem in Human Genetics" (Human Biology, Vol. 81, No. 1, pp. 3-11). Of 42,888 families with exactly two children, 9,523 had two girls, 22,031 had one girl and one boy, and 11,334 had two boys.

a) At the 1% significance level, do the data provide sufficient evidence to conclude that the distribution of genders in two-children families differs from the distribution predicted by the model described?

b) In view of your result from part (a), what conclusion can you draw?

Step 1 of Procedure 13.2 gives generic statements for the null and alternative hypotheses of a chi-square independence test. Use the terms statistically dependent and statistically independent, introduced on page 496, to restate those hypotheses.

In each of exercises 12.57-12.59, use the technology of your choice to solve the specified problems.

The Scottish Executive, Analytical Services Division Transport Statistics, compiles information on motorcycle accidents in Scotland. During one year, data on the number of motorcycle accidents, by day of the week and type of road (built-up or non built-up), are as presented on the WeissStats CD.
a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of day of the week within each type-of-road category and the marginal distribution of day of the week.
c. Determine the conditional distribution of type of road within each day of the week and the marginal distribution of type of road.
d. Does an association exist between the variables "day of the week" and "type of road" for these motorcycle accidents? Explain your answer.
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