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In Exercises 29鈥36, answer the given questions, which are related to percentages.

Chillax USA Today reported results from a Research Now for Keurig survey in which 1458 men and 1543 women were asked this: 鈥淚n a typical week, how often can you kick back and relax?鈥

a. Among the women, 19% responded with 鈥渞arely, if ever.鈥 What is the exact value that is 19% of the number of women surveyed?

b. Could the result from part (a) be the actual number of women who responded with 鈥渞arely, if ever鈥? Why or why not?

c. What is the actual number of women who responded with 鈥渞arely, if ever鈥?

d. Among the men who responded, 219 responded with 鈥渞arely, if ever.鈥 What is the percentage of men who responded with 鈥渞arely, if ever.鈥?

e. Consider the question that the subjects were asked. Is that question clear and unambiguous so that all respondents will interpret the question the same way? How might the survey be improved?

Short Answer

Expert verified

a. 293.17 respondents

b. No

c. 293 respondents

d. 15.0206%

e. The question must be framed to obtain responses in terms of the number of days.

Step by step solution

01

Given information

There are 1458 men and 1543 women in the survey.

The question of the survey is, 鈥淗ow often can you kick back and relax?鈥

02

Computing the equivalent value of percentage for women

a.

Of 1543 women, 19% responded, 鈥淩arely, if ever.鈥

The percentage symbol implies the value is divided by 100.

Here,19% of the total women surveyed are:

19%1543=191001543=293.17

Thus, the exact value is 293.17.

03

Criteria for the actual count of responses

b.

The actual count of women who responded 鈥渞arely, if ever鈥 is in decimal form. And the expected count is in the whole number.

Thus, the actual count cannot be 293.17.

04

Actual count of responses

c.

To estimate the closest actual count of responses, convert the decimal value to a whole number.

In this case, the rounded-off value is 293.

Thus, the actual number of the proposed responses is expected to be close to 293.

05

Computing the equivalent percentage value of the percent count

d.

Of 1458 men, 219 responded, 鈥淩arely, if ever.鈥

The fraction of men who gave this response is2191458.

The percentage is obtained by multiplying thefraction by 100.

Therefore,

219145810015.0206%

Thus, the percentage of men who responded is 15.0206%, approximately.

06

Comment on the question asked in the survey

e.

The question of the survey is, 鈥淚n a typical week,how often can you kick back and relax?鈥

Each respondent may interpret the question differently as it is asked in qualitative categories, one of them being 鈥渞arely, if ever.鈥

In such a case, the qualitative approach may lead to different interpretations.

The survey can be improved by asking responses in the quantitative format, that is, asking the number of days in a week.

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