Let's analyze each statement in detail:
### Statement 1: About 50% of everyone surveyed prefer a dog.
- We need to calculate the combined preference for a dog from both women and men.
- For women, 52% prefer dogs.
- For men, 51% prefer dogs.
- Combining these, the total preference for dogs is [tex]\( (0.52 \times 100 + 0.51 \times 100) / 200 = (52 + 51) / 200 = 103 / 200 = 0.515 \)[/tex], or 51.5%.
From the calculation, 51.5% of the surveyed people prefer dogs. Since "about 50%" generally implies a value that is acceptably close to 50% within a ±1% range, 51.5% falls outside this range. Hence, this statement is False.
### Statement 2: There appears to be an association between gender and pet preference.
- To determine if there is an association, we compare the preferences for each pet type between women and men:
- For dogs: 52% women vs. 51% men.
- For cats: 40% women vs. 39% men.
- For other pets: 8% women vs. 10% men.
There is a difference in the preferences for each pet type even though they appear to be relatively minor. The definition of an association typically allows for any noticeable differences in distribution preferences. Therefore, this statement is True.
### Statement 3: The data shows a significant difference in pet preference between women and men.
- To check for a significant difference, we look at the differences in the percentages:
- Dogs: |52% - 51%| = 1%
- Cats: |40% - 39%| = 1%
- Other pets: |8% - 10%| = 2%
All these differences (1% for dogs, 1% for cats, and 2% for other pets) are relatively small. We generally consider a difference significant if it exceeds 5%. Hence, this statement is False.
Therefore, the final answers are:
[tex]\[
\begin{tabular}{|l|l|}
\hline & True/False \\
\hline About 50% of everyone surveyed prefer a dog. & False \\
\hline There appears to be an association between gender and pet preference. & True \\
\hline The data shows a significant difference in pet preference between women and men. & False \\
\hline
\end{tabular}
\][/tex]
