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Chapter 12: Q. 21 (page 522)

Economy in Recession? The Quinnipiac University Poll conducts nationwide surveys as a public service and for research. This problem is based on the results of one such poll. Independent simple random samples of registered Democrats, Republicans, and Independents were asked, "Do you think the United States economy is in a recession now?' Of the 628 Democrats sampled, 220 responded "yes, as did 349 of the 471 Republicans sampled and 342 of the 646 Independents sampled. At the 1 % significance level, do the data provide sufficient evidence to conclude that a difference exists in the percentages of registered Democrats, Republicans, and Independents who. thought the U.S. economy was in a recession at the time?

Short Answer

Expert verified

The first 44 presidents of the United States are divided into five age groups of equal breadth. In other words, the class breadth of 5 is used to create the relative frequency distribution. The stem-and-leaf graphic is made of of lines per stem. As a result, the stem-and-leaf diagram is found to correlate to the relative frequency distribution.

Step by step solution

01

Explanation

Make a stem-and-leaf diagram for the ages of the first 44 presidents of the United States using MINITAB, using one line per stem.

Procedure for MINITAB:

Step 1: Go to Graph > Leaf and stem.

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

Step 3: In the Increment box, type 10.

Step 3: Choose OK.

02

Output

Stem-and-Leaf Display: AGE

Stem-and-leaf of AGE N=44

Leaf Unit =1.0

94236677899
(25)90011112244444555566677778
1060111244589

The stem contains only one line per stem, according to the MINITAB output. The president's age spans from 42 to 69 years old. In addition, the data's last digit symbolizes the leaf, while the first digit represents the stem.

03

Procedure

Make a stem-and-leaf diagram for the ages of the first 44 presidents of the United States using MINITAB, using two lines per stem.

Procedure for MINITAB:

Step 1: Select Graph>Stem and leaf

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

Step 3: In the Increment box, type 5.

Step 3: Choose OK.

04

Output

Stem-and-Leaf Display: AGE

Stem-and-leaf of AGE N=44

Leaf Unit =1.0

2423
946677899
2250011112244444
225555566677778
1060111244
36589

The stem contains only one line per stem, according to the MINITAB output. The president's age spans from 42 to 69 years old. In addition, the data's last digit symbolizes the leaf, while the first digit represents the stem.

05

Explanation

The first 44 presidents of the United States are divided into five age groups of equal breadth. In other words, the class breadth of 5 is used to create the relative frequency distribution. The stem-and-leaf graphic is made of of lines per stem. As a result, the stem-and-leaf diagram is found to correlate to the relative frequency distribution.

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Most popular questions from this chapter

How do you identify different chi-square distributions?

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

The National Governors Association publishes information on U.S Governors in Governors' Political Afflitiation and Term of Office. Based on that document we obtain the data on region of reidence an political party given on WeissStats site.

a. Group the bivariate data for these two variables into a contingency table.
b. Determine the conditional distribution of region within each party and the marginal distribution of region.
c. Determine the conditional distribution of party within each region and the marginal distribution of party.
d. Are the variables "region" and "party" for U.S. governors associated? Explain your answer.

Primary Heating Fuel. According to Current Housing Reports, published by the U.S. Census Bureau, the primary heating fuel for all occupied housing units is distributed as follows.

Suppose that you want to determine whether the distribution of primary heating fuel for occupied housing units built after 2010 differs from that of all occupied housing units. To decide, you take a random sample of housing units built after 2010 and obtain a frequency distribution of their primary heating fuel.

a. Identify the population and variable under consideration here.

b. For each of the following sample sizes, determine whether conducting a chi-square goodness-of-fit test is appropriate and explain

your answers: 200; 300; 400.

c. Strictly speaking, what is the smallest sample size for which conducting a chi-square goodness-of-fit test is appropriate?

Although the chi-square homogeneity test and the chi-square independence test use essentially the same basic procedure, the context of the two tests are quite different. Explain the difference.

Education of Prisoners. Refer to Exercise 12.49.

a. Find the conditional distribution of educational attainment with in each type of prison facility.

b. Does an association exist between educational attainment and of prison facility for prisoners? Explain your answer.

c. Determine the marginal distribution of educational attainment for prisoners.

d. Construct a segmented bar graph for the conditional distributions of educational attainment and marginal distribution of educational attainment that you obtained in parts (a) and (c), respectively. Interpret the graph in light of your answer to part (b).

e. Without doing any further calculations, respond true or false to the following statement and explain your answer: "The conditional distributions of facility type within educational attainment categories are identical."

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i. Find the percentage of prisoners in federal facilities who have at most an 8th-grade education.
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