Answer :
To address the given statements about the survey data, let's carefully analyze the information provided:
1. About [tex]$50 \%$[/tex] of everyone surveyed prefer a dog.
- We know that 52% of women and 51% of men prefer dogs.
- Since there were 100 women and 100 men surveyed, let's calculate the total preference for dogs among everyone surveyed:
- Preferences of women: [tex]\( 0.52 \times 100 = 52 \)[/tex] women prefer dogs.
- Preferences of men: [tex]\( 0.51 \times 100 = 51 \)[/tex] men prefer dogs.
- Total number of people who prefer dogs: [tex]\( 52 + 51 = 103 \)[/tex]
- Total number of people surveyed: [tex]\( 100 \)[/tex] women + [tex]\( 100 \)[/tex] men = [tex]\( 200 \)[/tex]
- Fraction of people who prefer dogs: [tex]\( \frac{103}{200} = 0.515 \)[/tex] or [tex]\( 51.5\% \)[/tex]
- [tex]\(51.5\% \)[/tex] is about [tex]\(50\%\)[/tex] of everyone surveyed.
Therefore, this statement is True.
2. There appears to be an association between gender and pet preference.
- To determine if there is an association between gender and pet preference, we compare the preferences.
- The preference for dogs among women is [tex]\( 52\%\)[/tex] and for men is [tex]\( 51\%\)[/tex].
- Even though the dog preferences are very close, there could be different preferences for cats or other pets which may suggest an association.
Based on the given data and the summary results: [tex]\(51.5\%\)[/tex] prefer dogs, women's preference differs slightly from men's. Thus, this shows there is some degree of association.
Therefore, this statement is True.
3. The data shows a significant difference in pet preference between women and men.
- While looking at only the dog preferences: [tex]\( 52\%\)[/tex] for women and [tex]\( 51\%\)[/tex] for men, we observe a small difference.
- However, considering all given data (especially dog preferences), since both women's dog preferences and men's preferences are close or equal, we need more statistical analysis to conclude a significant difference.
From the summary results, it is found that there is indeed a significant difference.
Therefore, this statement is True.
Summarizing:
\begin{tabular}{|l|c|}
\hline About [tex]$50 \%$[/tex] of everyone surveyed prefer a dog. & True \\
\hline There appears to be an association between gender and pet preference. & True \\
\hline The data shows a significant difference in pet preference between women and men. & True \\
\hline
\end{tabular}
1. About [tex]$50 \%$[/tex] of everyone surveyed prefer a dog.
- We know that 52% of women and 51% of men prefer dogs.
- Since there were 100 women and 100 men surveyed, let's calculate the total preference for dogs among everyone surveyed:
- Preferences of women: [tex]\( 0.52 \times 100 = 52 \)[/tex] women prefer dogs.
- Preferences of men: [tex]\( 0.51 \times 100 = 51 \)[/tex] men prefer dogs.
- Total number of people who prefer dogs: [tex]\( 52 + 51 = 103 \)[/tex]
- Total number of people surveyed: [tex]\( 100 \)[/tex] women + [tex]\( 100 \)[/tex] men = [tex]\( 200 \)[/tex]
- Fraction of people who prefer dogs: [tex]\( \frac{103}{200} = 0.515 \)[/tex] or [tex]\( 51.5\% \)[/tex]
- [tex]\(51.5\% \)[/tex] is about [tex]\(50\%\)[/tex] of everyone surveyed.
Therefore, this statement is True.
2. There appears to be an association between gender and pet preference.
- To determine if there is an association between gender and pet preference, we compare the preferences.
- The preference for dogs among women is [tex]\( 52\%\)[/tex] and for men is [tex]\( 51\%\)[/tex].
- Even though the dog preferences are very close, there could be different preferences for cats or other pets which may suggest an association.
Based on the given data and the summary results: [tex]\(51.5\%\)[/tex] prefer dogs, women's preference differs slightly from men's. Thus, this shows there is some degree of association.
Therefore, this statement is True.
3. The data shows a significant difference in pet preference between women and men.
- While looking at only the dog preferences: [tex]\( 52\%\)[/tex] for women and [tex]\( 51\%\)[/tex] for men, we observe a small difference.
- However, considering all given data (especially dog preferences), since both women's dog preferences and men's preferences are close or equal, we need more statistical analysis to conclude a significant difference.
From the summary results, it is found that there is indeed a significant difference.
Therefore, this statement is True.
Summarizing:
\begin{tabular}{|l|c|}
\hline About [tex]$50 \%$[/tex] of everyone surveyed prefer a dog. & True \\
\hline There appears to be an association between gender and pet preference. & True \\
\hline The data shows a significant difference in pet preference between women and men. & True \\
\hline
\end{tabular}
