When evaluating a report, Lance saw that 58% of the respondents to a survey think that the school year should be lengthened, while 42% think it should remain the same. The margin of error of the survey was ±10%. Which statement is true?

A. The population proportion of those who think the school year should be lengthened is definitely greater than the proportion of those who think it should remain the same.

B. The population proportion of those who think the school year should be lengthened is definitely less than the proportion of those who think it should remain the same.

C. The population proportion of those who think the school year should be lengthened is definitely equal to the proportion of those who think it should remain the same.

D. The population proportion of those who think the school year should be lengthened may or may not be less than the proportion of those who think it should remain the same.

Question

Mathematics

Adalynn Mason

28 April, 00:04

When evaluating a report, Lance saw that 58% of the respondents to a survey think that the school year should be lengthened, while 42% think it should remain the same. The margin of error of the survey was ±10%. Which statement is true?

A. The population proportion of those who think the school year should be lengthened is definitely greater than the proportion of those who think it should remain the same.

B. The population proportion of those who think the school year should be lengthened is definitely less than the proportion of those who think it should remain the same.

C. The population proportion of those who think the school year should be lengthened is definitely equal to the proportion of those who think it should remain the same.

D. The population proportion of those who think the school year should be lengthened may or may not be less than the proportion of those who think it should remain the same.

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Answers (1)

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Fernanda Marshall · Answer 1

58% of the respondents think that the school year should be lengthened and 42% of the respondents think it should remain the same.

The margin of error is ±10%. This means the Population Proportion of respondents who think that the school year should be lengthened is 58 - 10 to 58 + 10 which becomes 48% to 68%.

Likewise, the Population Proportion of respondents who think that the school year should remain the same is from 32% to 52%.

The two ranges are slightly overlapping from 48% to 52%. The population proportion who think school year should be lengthened may or not be more than those who think it should remain the same.

It can also be stated as:

The population proportion of those who think the school year should be lengthened may or may not be less than the proportion of those who think it should remain the same.

If the population proportion of those who think school year should be lengthened is between 48% to 50%, the population proportion of those who think it should remain the same will be between 50% to 52% and will be greater than those who think year should be lengthened. For other case, the population proportion of those who think school year should be lengthened will be larger.

So, option D gives the correct answer.