For Exercise 9.1, see page 191; for Exercise 9.2, see page 194.
9.3 Academic good standing. To be in good standing at college, a student needs to maintain a certain grade point average (GPA). Typically, a student who falls below 2.0 is put on academic probation for at least a semester. At a local college, administrators wanted to increase the GPA to remain in good standing from 2.0 and reported that the anticipated increase of on probation students would be from 3% to 5% of the student body. Relatively speaking, the increase in the percentage of students at the college who would be on academic probation would be
(a) 2% over the current figure.
(b) 40% over the current figure.
(c) 67% over the current figure.
(d) We cannot determine the percentage increase because we do not know how many students attend the college.
9.4 HIV infection rates. According to a June 2015 report by the Centers for Disease Control and Prevention (CDC), one in eight Americans with HIV do not know that they are infected with the virus. The night the report was released, a news station reported “1 in 8 Americans do not know that they are infected with HIV.” What is wrong with the news station’s reporting? (Note: More than one answer is possible.)
(a) Nothing is wrong. The news station reported exactly the information it should have.
(b) The news station’s report implies that one in eight Americans are infected with HIV.
(c) The news station’s report implies that one in eight Americans who have not been tested for HIV actually are infected with HIV.
(d) The news station’s report omitted the important piece of information that the one in eight figure is for those who are infected with HIV.
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9.5 Decreasing household trash. A large city has started a new recycling program that aims to reduce household trash by 25% by educating residents about more household items that can be recycled. A friend of yours says, “This is great! The amount of recycling will increase by 25%. That’s a great start!” What is wrong with your friend’s comment?
(a) Your friend assumed that the amount of trash and the amount of recycling was equal to begin with.
(b) We know that a 25% reduction in household trash will result in less than a 25% increase in recycling.
(c) We know that a 25% reduction in household trash will result in more than a 25% increase in recycling.
(d) None of the above.
9.6 Increasing test scores. The average score on an exam in organic chemistry was 60. The professor gave a retest and reported that the average score on the exam increased by 25%. This means that the average score on the retest was
(a) 45%.
(b) 75%.
(c) 85%.
(d) It is impossible to know without having all of the scores from the retest.
9.7 Classes on Fridays. A professor is concerned that not enough courses at his college hold class meetings on Fridays. After speaking with administrators, the professor finds out that 15% of courses have class meetings on Fridays. At this school, classes meet on either Monday-Wednesday-Friday or Tuesday-Thursday and do not meet on Saturday or Sunday.
(a) The 15% figure is about right because Friday is one of seven days of the week.
(b) The 15% figure is low because it is less than 20%, and Friday is one of five days on which classes meet.
(c) We cannot make a decision about the 15% figure because we do not know how courses are divided among teaching days (e.g., Monday-Wednesday-Friday or Tuesday-Thursday).
(d) The 15% figure is high because students tend to skip classes on Fridays.