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Chapter 5: Problem 53

Consider a survey in Pet Palace magazine in which single adults were asked if they own a dog or a cat. The results are shown in the contingency table. $$\begin{array}{lcc}\hline & \text { Dog } & \text { Cat } \\\\\hline \text { Female } & 16 & 41 \\ \text { Male } & 53 & 11 \\\\\hline\end{array}$$ Answer the following questions. Round to the nearest whole percentage as necessary. What percentage of those in the survey own a cat and are female?

Short Answer

Expert verified
Approximately 72\% of the females in the survey own a cat.

Step by step solution

01

Determine the total number of females surveyed

From the table provided, we see that 16 females own a dog and 41 females own a cat. To find the total number of females surveyed, we add these two values together: \[16 + 41 = 57\] Thus, there are 57 females surveyed.
02

Determine the number of females who own cats

According to the table, the number of females who own a cat is given as 41.
03

Calculate the percentage of females who own a cat

Now, divide the number of females who own a cat by the total number of females surveyed, and multiply by 100 to find the percentage:\[\left( \frac{41}{57} \right) \times 100 \approx 71.93\%\]Rounding to the nearest whole percentage, we get 72\%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Survey Interpretation
In any research, understanding survey results is crucial. Imagine a survey set up by Pet Palace magazine, targeting single adults to determine if they own a dog or a cat. The results are provided in what is called a "contingency table". This kind of table helps organize data in categories across two or more variables, allowing easy comparison. When interpreting such a table, pay attention to:
  • Rows, which in this case represent gender (Female and Male)
  • Columns, which categorize pet ownership (Dog and Cat)
Going through such tables step-by-step helps to break down how many people belong to each category, making it easier to interpret and analyze the survey results.
Percentage Calculation
Calculating percentages from a contingency table is a powerful method for understanding the share each group represents within an entire category. For instance, you might want to know what percentage of females surveyed in the Pet Palace magazine own a cat. Here's how you can do it:
  • First, identify the total number of females based on their pet ownership (16 own dogs and 41 own cats). So, 57 females were surveyed in total.
  • Next, focus on the group of interest. Here, it鈥檚 the 41 females who own cats.
  • Calculate the percentage: divide the number of females owning cats by the total number of females (41 divided by 57), then multiply by 100 to convert to a percentage.
  • Lastly, rounding up the calculation gives approximately 72%.
This step-by-step percentage calculation helps in understanding the proportion each subgroup contributes to the total population surveyed.
Data Classification
Data classification in surveys involves organizing information into relevant categories for better analysis. In the Pet Palace magazine example, classification helps us understand demographic trends among pet owners:
  • Gender Classification: Data is split between Female and Male respondents, making it easier to analyze gender-specific trends.
  • Pet Type Classification: Ownership is divided into Dog and Cat, allowing us to quickly see preferences.
Effective classification leads to clear insights. For instance, understanding how many females own cats involves noting the overlap of gender and pet categories. Proper classification allows one to efficiently identify patterns and correlations in the data, which can be critical for making informed decisions or drawing conclusions from a survey.

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Most popular questions from this chapter

A box of 20 pieces of taffy has 12 that are pink and 8 that are yellow. In how many ways can a handful of 12 pieces of taffy be pulled out so that half are pink and half are yellow?

Consider a March 2015 Gallup poll in which 1025 randomly chosen American adults were asked if they believe that more emphasis should be placed on traditional sources of energy, such as fossil fuels and nuclear energy, or on alternative energy sources, such as wind and solar energy. The respondents were also asked to classify their party affiliation. The results are shown in the contingency table. $$\begin{array}{lccc}\hline & \begin{array}{c}\text { More Traditional } \\\\\text { Sources }\end{array} & \begin{array}{c}\text { More Alternative } \\\\\text { Sources }\end{array} & \text { Total } \\\\\hline \text { Democrat } & 107 & 498 & 605 \\\\\text { Republican } & 252 & 168 & 420 \\ \text { Total } & 359 & 666 & 1025 \\\\\hline\end{array}$$ Answer the following questions. Round to the nearest whole percentage as necessary. What percentage of those in the survey said that more emphasis should be placed on alternative energy sources and are Republicans?

Consider the following group of bivariate values: $$\begin{array}{lllllll} \hline x_{1}=1.42 & x_{2}=1.48 & x_{3}=1.52 & x_{4}=1.5 & x_{5}=1.41 & x_{6}=1.42 & x_{7}=1.49 \\ y_{1}=1.38 & y_{2}=1.44 & y_{3}=1.48 & y_{4}=1.45 & y_{5}=1.36 & y_{6}=1.39 & y_{7}=1.44 \\ \hline \end{array}$$ Compute the following partial sums. $$\sum_{i=1}^{6} x_{i} y_{i}$$

Combine the Multiplication Principle and combinations to answer the questions.Powerball is a multistate game in which a player picks 5 balls numbered from 1 to 69 , then the Powerball that is a number from 1 to 26. How many different ways can the Powerball numbers be picked?

Consider the following group of bivariate values: $$\begin{array}{lllllll} \hline x_{1}=1.42 & x_{2}=1.48 & x_{3}=1.52 & x_{4}=1.5 & x_{5}=1.41 & x_{6}=1.42 & x_{7}=1.49 \\ y_{1}=1.38 & y_{2}=1.44 & y_{3}=1.48 & y_{4}=1.45 & y_{5}=1.36 & y_{6}=1.39 & y_{7}=1.44 \\ \hline \end{array}$$ Compute the following partial sums. $$\sum_{i=1}^{5} y_{i}$$
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