In Exercises 37–44, answer the given questions, which are rela...

Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Marriage Proposals 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?

Accepted Answer

All right, hello, everyone. So this question says, in a survey conducted by the National Nutrition Council, 1340 adults were asked about the importance of eating breakfast daily. Among the 1340 respondents, 52% stated that it is imperative to eat breakfast daily. Part A is asking to determine the exact value that is 52% of 1340 participants. Part B is asking, could the result from the preceding part be the actual number of survey respondents who said that eating breakfast daily is essential? Why or why not? And here we have 4 different answer choices labeled A through D, proposing not only the value for Part A, but also a yes or no explanation as to why or why. Not In terms of why the answer for part A can or cannot be expressed as the actual number of respondents. So first, to understand the answer to Part A, you have to understand how to calculate a percentage. Now, a percentage is a portion of a greater whole. And so the percentage Of something is going to be equal to the number that represents that part divided by the greater total. And then multiplied by 100. In this particular case, we're already given the percentage. And so when you're trying to find. What value represents a certain percentage of a greater number. What you do is multiply that number by the percentage itself, but as a fraction. Because going back to the original formula. Dividing the part by the total number should give you a percentage which you then. Multiply by 100. First, what I can do is take my percentage, in this case 52, and divide that by 100. They give me the original decimal, 0.52. So now, because I want to find 52% of 1340. I would multiply 1340 by 52% as a decimal, so by 0.52%. And that ultimately gives me 696.8. 696.8 is therefore the answer to part A. So now, Part B is about taking the number you just calculated for part A and applying it to the context of your data set. Right, because here, what you're doing is applying this number to a sample size. You're talking about a certain number of people that responded a certain way to your survey. So, when it comes to counting people, right, you must use integers, you must use whole numbers because you cannot count a fraction of a person. So therefore, if the number you calculated. Ends up being a decimal, you would have to go ahead and round to the nearest whole number. So here, 696.8 would become 697.0 whole respondents. And this happens pretty frequently, right? Oftentimes, percentages result in non-whole values when applied to a sample size. So it's important to go ahead and round to the nearest integer to make your number make sense in the context of the greater data set. So therefore Right, your answer. Is going to be option A in the multiple choice. For Part A, the value is 696.8. And for Part B, you would say no, because the actual number must be a whole number, so it would be rounded to 697.0. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

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Key Concepts

Percentage Calculation

Sample Size and Representation

Interpreting Survey Results

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