To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that  students had a laptop; therefore,  needs to go in the "laptop" column as the row total. Next, we were told that of those students,  owned a car; therefore, we need to put  in the "laptop" column and in the "car" row. Then, we were told that  students do not own a laptop, but own a car, so we need to put  in the "no laptop" column and the "car" row. Finally, we were told that  students do not have a laptop or a car, so  needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following: 

Our question asked how many students have a car. We add up the numbers in the "car" row to get the total:

This means that  students have a car.

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the honor roll. The first bit of information that we were given from the question was that  students had a curfew; therefore,  needs to go in the "curfew" column as the row total. Next, we were told that of those students,  were on the honor roll; therefore, we need to put  in the "curfew" column and in the "honor roll" row. Then, we were told that  students do not have a curfew but were on the honor roll, so we need to put  in the "no curfew" column and the "honor roll" row. Finally, we were told that  students do not have a curfew or were on the honor roll, so  needs to go in the "no curfew" column and "no honor roll" row. If done correctly, you should create a table similar to the following:

Our question asked how many students did not have a curfew. We add up the numbers in the "no curfew" column to get the total:

This means that  students do not have a curfew.

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the honor roll. The first bit of information that we were given from the question was that  students had a curfew; therefore,  needs to go in the "curfew" column as the row total. Next, we were told that of those students,  were on the honor roll; therefore, we need to put  in the "curfew" column and in the "honor roll" row. Then, we were told that  students do not have a curfew but were on the honor roll, so we need to put  in the "no curfew" column and the "honor roll" row. Finally, we were told that  students do not have a curfew or were on the honor roll, so  needs to go in the "no curfew" column and "no honor roll" row. If done correctly, you should create a table similar to the following:

Our question asked how many students were on the honor roll. We add up the numbers in the "honor roll" row to get the total:

This means that  students were on the honor roll.

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that  students were athletes; therefore,  needs to go in the "athlete" column as the row total. Next, we were told that of those students,  drinks soda; therefore, we need to put  in the "athlete" column and in the "drinks soda" row. Then, we were told that  students were not athletes, but drink soda, so we need to put  in the "not an athlete" column and the "drinks soda" row. Finally, we were told that  students are not athletes or soda drinkers, so  needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following:

Our question asked how many students drink soda. We add up the numbers in the "drinks soda" row to get the total:

This means that  students drink soda.

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that  students were athletes; therefore,  needs to go in the "athlete" column as the row total. Next, we were told that of those students,  drinks soda; therefore, we need to put  in the "athlete" column and in the "drinks soda" row. Then, we were told that  students were not athletes, but drink soda, so we need to put  in the "not an athlete" column and the "drinks soda" row. Finally, we were told that  students are not athletes or soda drinkers, so  needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following:

Our question asked how many students don't drink soda. We add up the numbers in the "doesn't drink soda" row to get the total, but first, we need to fill in a gap in our table, students who were athletes, but don't drink soda. We can take the total number of students who are athletes, , and subtract the number of students who drink soda, 

This means that  students who are athletes, don't drink soda.  

Now, we add up the numbers in the "doesn't drink soda" row to get the total:

This means that  students don't drink soda.

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.”  

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.

Answer: Select 20 students from each school and survey each student selected about how happy they are with the variety of cafeteria options. Particularly because the company believes that the happiness will range from school to school, it is important to have a sample from each school so that the company has insight into each school’s preferences. Note that while visiting each of the 20 schools might also give insight into the preferences at each school, observing that only one one day gives too narrow a sample to understand how students feel about the variety of options, since presumably each student will only be eating one meal that day.

Answer: More than half of all teachers chose Sharks as the new school’s mascot.  We are told that 80% of all teachers voted, and of those 80% who voted 70% chose Sharks. That means that 56% of all teachers chose Sharks, which is more than half.

Of the other choices, note that we don’t know whether there are more students or teachers, and it’s at least possible that there are quite a few more teachers than students. If, for example, there are 1,000 students and 50 teachers, then that would mean 200 students voted and 100 of them chose Bears, whereas only 28 teachers chose Sharks -- the big advantage that Sharks has among teacher voters is inconsequential if the students far outnumber the teachers, so “Sharks received the greatest number of votes” and “more teachers than students participated” are not necessarily true. 

We also cannot conclude that if all the students had voted, Bears would have won: for one, we don’t know that students far outnumber the teachers, and secondly we also don’t know how those 80% of students who did not vote would have voted.

Answer: The sampling method used by the researcher is flawed and may produce a biased estimate of the average number of pets per household in Los Gatos.

An important consideration here is that the researcher only surveyed people who were already at a pet supply store, so the sample she chose consisted entirely of people very likely to have at least one pet. People without pets rarely ever go to buy pet supplied! So her sample is likely to give a biased estimate, since it likely left out lots of people who would have had 0 pets.