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Income and Residence. The U.S. Census Bureau compiles information on money income of people by type of residence and publishes its finding in Current Population Reports. Independent simple random samples of people residing inside principal cities (IPC), outside principal cities but within metropolitan areas (OPC), and outside metropolitan areas (OMA), gave the following data on income level.

Residence
Income

IPCOPCOMATotal
Under \(15,000
7510646227
\)15,000-\(34,99910616161328
\)35,000-\(74,9999818352333
\)75,000 and over4810214164
Total
3275521731052

a. Identify the populations under consideration.

b. Identify the variable under consideration.

c. At the 5% significance level, do the data provide sufficient evidence to conclude that people residing in the three types of residence are non homogeneous with respect to income level?

Short Answer

Expert verified

It is obvious from the dot plot that there are more presidents between the ages of 50 and 58. The dot plot also reveals a roughly symmetric distribution.

Step by step solution

01

Given Definition

Create a dotplot for the ages of the first 44 presidents of the United States using MINITAB.

Procedure for MINITAB:

Step 1: Select Dotplot from the Graph menu.

Step 2: Click OK after selecting One Y-Simple.

Step 3: In the Graph variables section, type the relevant DATA column.

Step 4: Click the OK button.

02

Output

MINITAB OUTPUT:

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Most popular questions from this chapter

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution: 0.2, 0.4, 0.3, 0.1

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Significance level = 0.05

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

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Significance level=0.01

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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?

What is meant by saying that a variable has a chi-square distribution?

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