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Answer the given questions, which are related to percentages. In a survey conducted by TheKnot.com, 1165 engaged or married women were asked about the importance of a bended knee when making a marriage proposal. Among the 1165 respondents, \(48 \%\) said that the bended knee was essential. a. What is the exact value that is \(48 \%\) of 1165 survey respondents? b. Could the result from part (a) be the actual number of survey subjects who said that a bended knee is essential? Why or why not? c. What is the actual number of survey respondents saying that the bended knee is essential? d. Among the 1165 respondents, 93 said that a bended knee is corny and outdated. What percentage of respondents said that a bended knee is corny and outdated?

Step by step solution

01

Calculate 48% of 1165

To find 48% of 1165, multiply 1165 by 0.48: \[ 1165 \times 0.48 = 559.2 \]

02

Determine if 559.2 is a possible survey result

Since the number of respondents must be a whole number, 559.2 cannot be the exact number of survey subjects who said that a bended knee is essential.

03

Round to the nearest whole number

Rounding 559.2 to the nearest whole number, we get 559. Therefore, the actual number of respondents saying that bended knee is essential is 559.

04

Calculate percentage for 93 respondents

To find the percentage of the 93 respondents who said that a bended knee is corny and outdated, use the formula \[ \left( \frac{93}{1165} \right) \times 100 \approx 7.98\text{\text{%}} \]

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Key Concepts

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

Survey Analysis

Surveys are critical tools in statistics. They allow us to gather data from a specific group to understand opinions or behaviors. In this example, TheKnot.com surveyed 1165 engaged or married women about marriage proposals. The goal was to find out how many women believe a bended knee is essential. It's important to note that survey results can help infer broader population trends but should be analyzed correctly to avoid errors and misinterpretations.
When analyzing survey data, understanding the sample size and the population it represents is crucial. Here, the sample size is 1165 respondents, which can provide statistically significant insights if the sample is diverse and representative of the overall population.

Percentage Calculation

Calculating percentages is a fundamental skill in statistics. It allows us to express a part of the whole in a way that's easy to understand. Here, we needed to find what 48% of 1165 respondents is.
First, convert the percentage to a decimal by dividing by 100. So, 48% becomes 0.48. Then, multiply this decimal by the total number of respondents: \ \(1165 \times 0.48 = 559.2\).
This calculation gives us 559.2, but since you can't have a fraction of a respondent, further steps are needed to make sense of this number in context.

Whole Number Rounding

In statistics, sometimes you get results that aren't whole numbers, which isn't practical in situations where you count people. Here, we calculated that 559.2 respondents consider a bended knee essential. But there can't be 0.2 of a person.
To solve this, we round the number to the nearest whole number. Since 0.2 is less than 0.5, we round down. This means 559.2 becomes 559. So, 559 respondents said a bended knee is essential. Knowing when and how to round numbers appropriately prevents inaccuracies in reporting and analysis.

Statistical Respondents

Statistical respondents are the people who participate in a survey. Each respondent's input contributes to the overall findings. Understanding how to handle responses correctly is key.
In this survey, out of 1165 respondents, we identified two specific responses: 559 who said a bended knee is essential and 93 who said it's corny and outdated. Calculating the percentage of respondents who find it corny involves the formula: \ \( \left( \frac{93}{1165} \right) \times 100 \approx 7.98\text{\text{%}}\ \).
This is about 8%, showcasing a minority perspective. It's important to accurately account for each respondent's input, enabling clear and meaningful statistical analyses.