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All SAT Mathematics Resources

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Want to review SAT Mathematics but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different SAT Mathematics flashcards! Our SAT Mathematics flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous SAT Mathematics flashcards.

Flashcards: Drawing Logical Conclusions

A student wants to find out whether mothers in his city support a local initiative to redesign the city’s largest park. He decides to conduct a poll on this question by calling the home phone numbers of all 300 students in his private high school, asking to speak to their mothers, and recording their responses as yes, no, or no preference. Of the calls, 250 were answered and 200 mothers responded “yes,” with 40 saying “no” and 10 saying “no preference.”

Does this survey lead to the conclusion that most mothers in the city support the initiative to redesign the park?

No, because the mothers of private high school students may not be representative of all mothers in the city.

No, because we do not know how the mothers who did not answer the phone would have responded.

Yes, because there are five times as many “yes” answers as “no” answers.

Yes, because 80% of the mothers who answered are in favor of the initiative.

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Flashcards: Drawing Logical Conclusions

Does this survey lead to the conclusion that most mothers in the city support the initiative to redesign the park?

Your answer:

No, because we do not know how the mothers who did not answer the phone would have responded.

Your answer:

Yes, because there are five times as many “yes” answers as “no” answers.

Your answer:

Yes, because 80% of the mothers who answered are in favor of the initiative.

Correct answer:

No, because the mothers of private high school students may not be representative of all mothers in the city.

Explanation:

Answer: No, because the mothers of private high school students may not be representative of all mothers in the city.

It is important to note here that the group of people the conclusion is about - “mothers in the city” - is not the same as the group of people surveyed. The people surveyed were mothers of private school students (which means we don’t know what mothers of public school students would have thought) and of high school students (so we don’t know what mothers of younger students would have thought). This creates too narrow of a sample to draw a conclusion about the larger population of “all mothers in the city.”

Flashcards: Drawing Logical Conclusions

The marketing department of a chain of pet stores surveyed a random sample of American families about the number of pets they have. Using the sample data, the department estimates that 81% of families have at least one pet in their home. The margin of error for this estimation is 5%. Which of the following conclusions about all American families can most appropriately be drawn from this data?

The marketing department is between 76% and 86% confident that most American families have at least one pet in their home.

It is likely that between 76% and 86% of American families have at least one pet in their home.

More than 76% of American families have exactly one pet in their home.

No greater than 86% of American families have a pet in their home.

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Flashcards: Drawing Logical Conclusions

Your answer:

The marketing department is between 76% and 86% confident that most American families have at least one pet in their home.

Your answer:

More than 76% of American families have exactly one pet in their home.

Your answer:

No greater than 86% of American families have a pet in their home.

Correct answer:

It is likely that between 76% and 86% of American families have at least one pet in their home.

Explanation:

Answer: It is likely that between 76% and 86% of American families that have at least one pet in their home.

A margin of error creates a range between which the statistic is most likely to fall. Here the researchers’ best estimate of the percentage of American families with at least one pet is 81%, and if you add and subtract the 5% margin of error you arrive at a range of 76-86%, meaning that that range is where the true, exact percentage most likely falls. Note, however, that while it is very likely that the true statistic falls in that range it is not 100% guaranteed, so the conclusions that “no greater than 86%” or “more than 76%” go too far to be proven from this one survey.

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Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

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All SAT Mathematics Resources

Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

Flashcards: Drawing Logical Conclusions

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

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