Statistics Literacy

Test your ability to interpret statistical data.

Understanding and interpreting statistics is probably the most useful math skill that the typical average person can possess. A lot of people, even in the media, are lacking in this. How well do you do?

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* 1. Which of the following is a better study (not necessarily a flawless study)?

Alice is a professor of microbiology teaching at a university with over 50,000 students. This semester she is teaching an introductory class on microbiology that contains 300 students. During the semester she conducts a poll in her class, asking the students if they think vaccines are beneficial or not. 96% of the class thinks vaccines are mostly beneficial.

Bob is a political pollster working for a conservative think tank. He places a link to a survey on his think tank's social media, asking if people plan to vote for the conservative candidate in the upcoming election. Over 1,000 people respond, and it appears that 83% of people plan on voting for the conservative candidate. Bob concludes that that the conservative candidate has an 83% chance to win the upcoming election.

Claire is a Title IX consultant at a large corporation. She wants to know if a new policy about transgender people being allowed to use the restroom that comports with their gender identity is being well received. In order to control for bias, she makes sure not to send the survey to people who are known to be conservative Christians. According to the survey 79% of people are somewhat or very comfortable with the policy, and so Claire concludes that a large majority agree with the policy.

David is a high school student at a school with around 2,000 students. The school is having a student council election in a couple weeks. David asks ten of his friends if they would vote for him should he run for student council, and all ten say they would, making David feel very confident that he'll win the election.

Eve works in the marketing department for a large retail chain that is considering expanding into a new region. She wants to know how the people in this region feel about the retail chain and if they will be likely to shop there. She and her team obtain demographic data for the region and begin to make make phone calls to people of different ethnic and socioeconomic background in different parts of the region so that the distribution of the respondent's backgrounds reflections the demographics, and find that 62% of people have a positive attitude about the retail chain and so concludes that expansion is a good idea.

Frank is a casino owner who is trying to stop a law going through congress that would heavily regulate gambling in his state. To see if this law has popular support among the residents of his state he begins leaving surveys in the hotel rooms of his casino's patrons, with instructions saying that anyone who fills it out and hands it in will get a free $5.00 chip at the cage. After a week he compiles the data and finds that 89% of people are against the new law. Frank brings this to a state congressional hearing on the bill to show that it has extremely weak support among the residents of the state.

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* 2. A data analyst guessed that the average yearly income for people in their state was $50,000 USD. The analyst conducts a survey to test this hypothesis and concludes that they are correct. Which of the following were most likely to be the results obtained?

A survey of 500 people found that the average yearly income was $56,000 (S.D.=$9750; 95% C.I.)

A survey of 500 people found that the average yearly income was $43,000 (S.D.=$7500; 98% C.I.)

A survey of 500 people found that the average yearly income was $48,000 (S.D.=$11,700; 90% C.I.)

A survey of 500 people found that the average yearly income was $47,000 (S.D.=$15,700; 99% C.I.)

A survey of 500 people found that the average yearly income was $49,000 (S.D.=$9,200; 99% C.I.)

A survey of 1,000 people found that the average yearly income was $57,000 (S.D.=$13,300; 95% C.I.)

A survey of 100,000 people found that the average yearly income was $51,000 (S.D.=$10,000; 90% C.I.)

None of the above.

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* 3. What is the mean? What is the median? What is standard deviation?

The mean is what shows up most often. The median is the average. The standard deviation is the difference from a prediction.

The mean is the average. The median is the midpoint. The standard deviation is how spread out the data are from the average.

The mean is the center. The median is what shows up most often. The standard deviation is how far apart the mean and median are from each other.

The mean and median are words that mean the same thing, which is the average. The standard deviation is how spread out the data are from the average.

The mean is the point at which there are just as many data above as there is below it. The median is what shows up most often. The standard deviation tells you if something is an outlier or not.

The mean is the expected value. The median is the midpoint. The standard deviation is how many data are not in the expected value (the mean).

The mean are all the data that are not outliers. The median is the average. The standard deviation is the number of outliers.

The mean is the average. The median is the midpoint. The standard deviation tells you if your data are good or not.

The mean is the interquartile range. The median is the center of the interquartile range. The standard deviation is the outerquartile range.

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* 4. True or false: a hypothesis test is used to prove that a theory is true.

True

False

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* 5. True or false: most data will always be on or close to the average.

True

False

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* 6. In which of the following cases would you reject the null hypothesis? (select all that apply)

α=0.05; p=0.1

α=0.1; p=0.08

α=0.05; p=0.049

α=0.05; p=0.057

α=0.05; p≤0.0001

α=0.01; p≤0.05

α=0.05; p=0.023

α=0.05; p=0.051

α=0.05; p<0.05

α=0.05; p=0.04598939

α=0.05; p≤0.005

α=0.01; p=0.015

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* 7. What does it mean for the result of a study to be statistically significant?

The result is very large.

The result is the average.

The result has a large standard deviation.

There contain a lot of outliers.

The data are of great interest.

There is a bimodal distribution.

The result is unexpected.

There is a normal distribution.

The result was unlikely due to chance.

The result can be discarded.

The result cannot be discarded.

The result proves the theory is true.

The result proves the theory is not true.

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* 8. Studies show that most car accidents occur within a few miles of a person's residence. This means that a person driving 1 mile from home to the gas station is in more danger of getting in an accident than a person who is on vacation in another town driving 1 mile from a hotel to a gas station.

True

False

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* 9. True or false: obtaining a larger sample size will always reduce the standard deviation.

True

False