Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.