Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Observed Frequencies
\begin{tabular}{ccccc}
\hline Over 65 years & [tex]$45-65$[/tex] years & [tex]$25-44$[/tex] years & [tex]$15-24$[/tex] years & Under 15 years \\
\hline 94 & 282 & 549 & 235 & 408 \\
\hline
\end{tabular}

You wonder if the age distribution of people who are left-handed matches the age distribution of the US population. You obtain the following data from the 2000 census:
\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{Percent Distribution of the US Population by Age Group} \\
\hline Age Group & Over 65 years & [tex]$45-65$[/tex] years & [tex]$25-44$[/tex] years & [tex]$15-24$[/tex] years & Under 15 years \\
\hline Percent & [tex]$12.43 \%$[/tex] & [tex]$22.01 \%$[/tex] & [tex]$30.22 \%$[/tex] & [tex]$13.93 \%$[/tex] & [tex]$21.41 \%$[/tex] \\
\hline
\end{tabular}

[Source: Hobbs, F., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in the 20th century. US Census Bureau.]

You use a chi-square test for goodness of fit to see how well the sample of people who are left-handed fits the census data.

What is the most appropriate null hypothesis?

A. The distribution of ages among people who are left-handed is different from that provided by the census data.
B. The distribution of ages among people who are left-handed is equal across the five age categories.
C. The distribution of ages among people who are left-handed is not equal across the five age categories.
D. The distribution of ages among people who are left-handed is the same as that provided by the census data.

Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,568, if the null hypothesis is true:

Expected Frequencies
\begin{tabular}{ccccc}
\hline Over 65 years & [tex]$45-65$[/tex] years & [tex]$25-44$[/tex] years & [tex]$15-24$[/tex] years & Under 15 years \\
\hline & & & & & \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine the expected frequencies for a sample size of 1,568 based on the provided percent distribution of the US population by age group, we follow these steps:

1. Identify the Sample Size and Percent Distribution:
- Sample Size ([tex]\( n \)[/tex]) = 1,568
- Percent distribution:
- Over 65 years: [tex]\( 12.43\% \)[/tex]
- 45-65 years: [tex]\( 22.01\% \)[/tex]
- 25-44 years: [tex]\( 30.22\% \)[/tex]
- 15-24 years: [tex]\( 13.93\% \)[/tex]
- Under 15 years: [tex]\( 21.41\% \)[/tex]

2. Convert Percentages to Proportions:
- Convert each percentage into a proportion by dividing by 100.

For "Over 65 years":
[tex]\[ 12.43\% = 0.1243 \][/tex]

For "45-65 years":
[tex]\[ 22.01\% = 0.2201 \][/tex]

For "25-44 years":
[tex]\[ 30.22\% = 0.3022 \][/tex]

For "15-24 years":
[tex]\[ 13.93\% = 0.1393 \][/tex]

For "Under 15 years":
[tex]\[ 21.41\% = 0.2141 \][/tex]

3. Calculate the Expected Frequencies:
- Multiply each proportion by the sample size ([tex]\( n = 1,568 \)[/tex]) to obtain the expected frequency for each age group:

For "Over 65 years":
[tex]\[ 0.1243 \times 1568 = 194.9024 \][/tex]

For "45-65 years":
[tex]\[ 0.2201 \times 1568 = 345.1168 \][/tex]

For "25-44 years":
[tex]\[ 0.3022 \times 1568 = 473.8496 \][/tex]

For "15-24 years":
[tex]\[ 0.1393 \times 1568 = 218.4224 \][/tex]

For "Under 15 years":
[tex]\[ 0.2141 \times 1568 = 335.7088 \][/tex]

4. Present the Expected Frequencies:
We can now fill in the expected frequencies in the table:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Age Group} & \text{Expected Frequency} \\ \hline \text{Over 65 years} & 194.9024 \\ \hline \text{45-65 years} & 345.1168 \\ \hline \text{25-44 years} & 473.8496 \\ \hline \text{15-24 years} & 218.4224 \\ \hline \text{Under 15 years} & 335.7088 \\ \hline \end{array} \][/tex]

5. Formulating the Null Hypothesis:
The most appropriate null hypothesis (H₀) based on the data comparison would be:
[tex]\[ \text{The distribution of ages among people who are left-handed is the same as that provided by the census data.} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.