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Chapter 12: Q. 22 (page 522)

Yakashba Estates. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats site are data on lot size (in acres) and house size (in square feet) for homes in the Yakashba Estates, a private community in Prescott, AZ. We used the following codings for lot size and home size.

Lot size
House size
Size (acrs)CodingSize (sq. ft.)Coding
Under 2.25L1Under 3000H1
2.25-2.49L23000-3999H2
2.50-2.74L34000&overH3
2.75 & overL4

Use the technology of your choice to do the following tasks for the coded variables.

a. Group the bivariate data for the variables "lot size" and "house size" into a contingency table.

b. Find the conditional distributions of lot size by house size and the marginal distribution of lot size.

c. Find the conditional distributions of house size by lot size and the marginal distribution of house size.

d. Does an association exist between the variables "lot size" and "house size" for homes in the Yakashba Estates? Explain your answer.

Short Answer

Expert verified

As a result, it may be argued that part (b) of the stem-and-leaf diagram is more beneficial than part (a).

Step by step solution

01

Subpart (a) Step 1: Given Information

a)

Create a stem-and-leaf diagram for the number of pulses using MINITAB, using one line per stem.

Procedure for MINITAB:

Step 1: Select Graph > Stem & leaf .

Step 2: In the Graph variables, choose the PULSES column.

Step 3: In the Increment box, type 10.

Step 3: Choose OK.

02

Subpart (a) step 2:

MINITAB Output:

Stem-and-Leaf Display: PULSES

Stem-and-leaf of pULSES N=18

Leaf Unit =1.0

434778
840467
(9)5446677778
160

The stem contains only one line per stem, according to the MINITAB output. The number of pulses varies between 34 and 60. In addition, the data's last digit symbolises the leaf, while the first digit represents the stem.

03

Subpart (b) Step 1:

Create a stem-and-leaf diagram for the number of pulses using MINITAB, using one line per stem.

Procedure for MINITAB:

Step 1: Select Graph > Stem & leaf .

Step 2: In the Graph variables, choose the PULSES column.

Step 3: In the Increment box, type 5.

Step 3: Choose OK.

04

Subpart (b) Step 2:

MINITAB Output:

Stem-and-Leaf Display: PULSES

Stem-and-leaf of pULSES N=18

Leaf Unit =1.0

134
43778
6404
8467
(2)544
856677778
160

The stem contains only one line per stem, according to the MINITAB output. The number of pulses varies between 34 and 60. In addition, the data's last digit symbolises the leaf, while the first digit represents the stem.

05

Subpart (c) Step 1:

Explanation:

In part (a), the number of classes (stem) is fewer than in part (b) (b). Furthermore, for optimal distribution, the number of classes should be between five and fifteen. As a result, it may be argued that part (b) of the stem-and-leaf diagram is more beneficial than part (a).

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Most popular questions from this chapter

To decide whether two variables of a population are associated, we usually need to resort to inferential methods such as the chi-square independence test. Why?

In Exercises 12.101-12.106, tase either the critical-value approach or the P-value approach to perform a chi-square homogeneity test, provided the conditions for using the test are met.
12.101 Self-Concept and Sightedness. Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article "An Exploration into Self Concept: A Comrarative Analysis between the Adolescents Who Are Sighted and
Elind in India" (British Journal of Visual Impairment, Vol. 30, No. 1, of sighted and blind Indian adolescents gave the following data on self-concept.

a. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in self-concept distributions between sighted and blind Indian adolescents?
b. Repeat part (a) at the1%significance level.

12.50 U.S. Hospitals. The American Hospital Association publishes 12.30 U.S. information about U.S. hospitals and nursing homes in Hospital Statistics. The following contingency table provides a cross classification of U.S. hospitals and nursing homes by type of facility and number of beds.

In the following questions, the term hospital refers to either a hospital or nursing home.


24 or fewer25-7475 or moreTotal
General260158635575403
Psychiatric24242471737
Chronic132236
Tuberculosis0224
Other25177208410
Total310201042606580

a. How many hospitals have at least 75 beds?

b. How many hospitals are psychiatric facilities?

c. How many hospitals are psychiatric facilities with at least 75 beds?

d. How many hospitals either are psychiatric facilities or have at least 75 beds?

e. How many general facilities have between 25 and 74 beds?

f. How many hospitals with between 25 and 74 beds are chronic facilities?

g. How many hospitals have more than 24 beds?

School Enrollment. Refer to Exercise 12:48. For students below postsecondary, solve the following problems.

a. Determine the conditional distribution of level for each gender.

b. Determine the marginal distribution of level.

c. Are the variables "gender"" and "level" associated? Explain your answer

d. Find the percentage of students in nursery school.

e. Find the percentage of females in nursery school.

f. Without doing any further calculations, respond true or false to the following statement and explain your answer: "The conditional distributions of gender within levels are not identical " .

g. Determine and interpret the marginal distribution of gender and the conditional distributions of gender within levels.

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?
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