We appreciate your visit to June is a researcher who read a 2016 study that published the following population distribution for Americans tex begin tabular lrrrrrr Age group 0 18. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To perform a [tex]\(\chi^2\)[/tex] goodness-of-fit test, one of the conditions is that the expected counts in each category should be at least 5. Given a sample of 38 Americans and the official percentages, the expected count for an age group is calculated as
[tex]$$
\text{Expected Count} = (\text{Sample Size}) \times (\text{Percentage})
$$[/tex]
For each age group:
1. For the [tex]\(0-18\)[/tex] group:
[tex]$$
38 \times 0.24 = 9.12
$$[/tex]
This is greater than 5.
2. For the [tex]\(19-25\)[/tex] group:
[tex]$$
38 \times 0.09 = 3.42
$$[/tex]
This expected count is less than 5.
3. For the [tex]\(26-34\)[/tex] group:
[tex]$$
38 \times 0.12 = 4.56
$$[/tex]
This expected count is less than 5.
4. For the [tex]\(35-54\)[/tex] group:
[tex]$$
38 \times 0.26 = 9.88
$$[/tex]
This is greater than 5.
5. For the [tex]\(55-64\)[/tex] group:
[tex]$$
38 \times 0.13 = 4.94
$$[/tex]
This expected count is less than 5.
6. For the [tex]\(65+\)[/tex] group:
[tex]$$
38 \times 0.15 = 5.70
$$[/tex]
This is greater than 5.
Since the expected counts for the [tex]\(19-25\)[/tex], [tex]\(26-34\)[/tex], and [tex]\(55-64\)[/tex] age groups are less than 5, these categories fail the large counts condition.
Thus, the counts that cause the failure of the large counts condition are in the [tex]\(19-25\)[/tex], [tex]\(26-34\)[/tex], and [tex]\(55-64\)[/tex] groups.
The correct answer choices are:
C, D, and E.
[tex]$$
\text{Expected Count} = (\text{Sample Size}) \times (\text{Percentage})
$$[/tex]
For each age group:
1. For the [tex]\(0-18\)[/tex] group:
[tex]$$
38 \times 0.24 = 9.12
$$[/tex]
This is greater than 5.
2. For the [tex]\(19-25\)[/tex] group:
[tex]$$
38 \times 0.09 = 3.42
$$[/tex]
This expected count is less than 5.
3. For the [tex]\(26-34\)[/tex] group:
[tex]$$
38 \times 0.12 = 4.56
$$[/tex]
This expected count is less than 5.
4. For the [tex]\(35-54\)[/tex] group:
[tex]$$
38 \times 0.26 = 9.88
$$[/tex]
This is greater than 5.
5. For the [tex]\(55-64\)[/tex] group:
[tex]$$
38 \times 0.13 = 4.94
$$[/tex]
This expected count is less than 5.
6. For the [tex]\(65+\)[/tex] group:
[tex]$$
38 \times 0.15 = 5.70
$$[/tex]
This is greater than 5.
Since the expected counts for the [tex]\(19-25\)[/tex], [tex]\(26-34\)[/tex], and [tex]\(55-64\)[/tex] age groups are less than 5, these categories fail the large counts condition.
Thus, the counts that cause the failure of the large counts condition are in the [tex]\(19-25\)[/tex], [tex]\(26-34\)[/tex], and [tex]\(55-64\)[/tex] groups.
The correct answer choices are:
C, D, and E.
Thanks for taking the time to read June is a researcher who read a 2016 study that published the following population distribution for Americans tex begin tabular lrrrrrr Age group 0 18. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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