12 of 18 Items .... Type: Sensible?

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We started with this:

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Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position -- Do these situations make sense or not?

1. The Department of Education conducted an observational study to determine the average salary of high school teachers in each of the United States 


2. A paint company conducted a double-blind experiment to determine which of two types of exterior paint was more resistant to rain. 


3. The lab conducted an experiment to determine whether the throat culture was positive for strep. 


4. In a study of medications designed to slow the rate of balding in men, a placebo group had better results than the control group. 


5. A meta-analysis was conducted to determine the population of New Zealand. 


6. A case-control experiment was used to determine the average family size in Utah.

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Defend your answer! Here's your claim ... what's your warrant?

Give an example or a situation to bolster your position.

1. For a high school project, I conducted a census to determine the average rate that teenagers charge for babysitting. 


2. Even though the study used a convenience sample, the results may be meaningful. 


3. The study must have been biased, because it concluded that the 75% of Americans are more than 6 feet tall. 


4. We obtained a simple random sample of milk-producing cows in Jefferson County by drawing the names of 50 dairy farms from a hat and asking the owners of those farms to select three cows for us to study. 


5. A good strategy for stratified sampling involves first using simple random sampling to choose 500 people, then randomly dividing them into ten groups of 50 to represent the 10 strata. 


6. Although the study was conducted with a representative sample and careful analysis, the conclusions still reflect the researcher's anti-death penalty bias. 

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Defend your answer! Here's your claim ... what's your warrant?

Give an example or a situation to bolster your position.

1. When the IRS decided to determine how many people were cheating on their taxes, they did a study in which the sample consisted of every adult in the United States.


2. My professor conducted a study in which he was unable to measure any sample statistics, but he succeeded in determining the population parameters with a very small margin of error.


3. A poll conducted two weeks before the election found that Smith would get 70% of the vote, with a margin of error of 3%, but he ended up losing anyway.


4. The goal of a new startup company is to compete with Nielsen Media Research in compiling television ratings. They intend to succeed by providing data with a larger margin of error than Nielsen's while charging television stations the same price for their service.


5. The goal of the research is to learn about depression among people who have suffered through a family tragedy, so the population of interest is everyone who has been sick in the past month.


6. We know for certain that a majority of Americans support the President's position on this issue because an opinion poll found support from 65% of Americans, with a margin of error of 5%.

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Distribution Statements: Sensible or Not?

Defend your answer! Here's your claim ... what's your warrant?

1. Because this data has two modes, it cannot be symmetrical. 


2. This distribution is left-skewed because it has outliers to the left. 


3. Josh works at a veterinary clinic and weighs the dogs. He claims there is less variation in the weights of 10 Rottweilers than in the weights of 10 dogs of different breeds. 


4. Josh combines the weights of 10 toy poodles, 10 Rottweilers and 10 St. Bernards into one big group. He says the distribution has one mode. 


5. Jean concludes that the mean of her symmetric distribution is greater than the median. 

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Measures of Central Tendency Statements: Sensible or Not?

Defend your answer! Here's your claim ... what's your warrant?

Give an example or a situation to bolster your position 

1. A data set should be discarded if the mean exceeds the mode. 


2. A student with an average of 65 computes her new average after earning a 70 on the last exam. Her new average is 72. 


3. Observing that the mean weight of a group of patients is 154 pounds and the median weight is 145 pounds, the doctor concludes that there must be an outlier on the heavy side. 


4. Noting that there are three modes in his data set, Rob assumes there was an error in his data gathering. 


5. The two means in the data lie at 102 and 201


6. The two medians in the data set lie at 23 and 28. 


7. The two modes in the data set lie at 45 and 100. 

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Percent Statements: Sensible or Not?

Defend your answer! Here's your claim ... what's your warrant?

1. The percentage of households with more than four children decreased by 100,000 households


2. Brent makes 120% less than Bill each month 


3. Ann is 10% taller than Brenda, so Brenda is 10% shorter than Ann


4. Fifty percent of the people in the room are men and 50% of the people in the room are single. Therefore, 25% of the people in the room are single men.


5. Pete’s prices are 10% more than Paul’s prices, so Pete’s prices are 110% of Paul’s prices.


6. The interest rate at the bank increased by 100% 

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Error Statements: Sensible or Not?

Defend your answer! Here's your claim ... what's your warrant?

1. There are 138,232 species of butterflies and moths on the Earth. 


2. The measurement taken by an electronic timer must be more accurate than that taken by stopwatch. 


3. The relative error that a microbiologist makes in measuring a cell must be less than the relative error that an astronomer makes in measuring the width of a galaxy, because cells are smaller than galaxies. 


4. The bank teller claims that his errors are random even though they are always to his advantage. 


5. The 6 billionth person on Earth was born on October 12th 1999, in Bosnia 


6. I would rather be shortchanged by $1 than by 1% 

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So ... is this possible? Or is it a well-done fake?

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"Why do we call pi irrational when it's clearly the ratio of a circle's circumference to its diameter?" - Indira Gil.

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If an odd plus an odd is an even, then what about 1.5 + 1.5?

If it ends in an odd digit, shouldn't it be an odd number?

Is 1.5 odd ... or is it not classified?

The aide piped up, "Think of it as 1.50 - that's even."

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FiveThirtyEight had this graph
and the comment. "It looks to me as if Mr. Cain had been on a positive trajectory before, perhaps having moved up to about 28 percent of the Republican vote."




Is that blue trendline reasonable?

Some background information. From Wikipedia, "Cain ran as a Washington outsider and became a front-runner in the race in the fall of 2011. However, Cain's support plummeted after several women alleged that he had engaged in sexual harassment or, in one case, a 13-year extramarital affair. Cain and his wife unequivocally said the accusations were false, but Cain, citing the toll the allegations had taken on his family and his political support, suspended his campaign on December 3, 2011."

Cain died in August 2020, after contracting COVID-19 at a Trump rally.