Comparing Populations Math Lesson

Multiple Select

Lin wants to know if students in elementary school generally spend more time playing outdoors than students in middle school. She selects a random sample of size 20 from each population of students and asks them how many hours they played outdoors last week. Suppose that the MAD for each of her samples is about 3 hours.

Select **all** pairs of sample means for which Lin could conclude there is a meaningful difference between the two populations.

• elementary school: 12 hours, middle school: 10 hours

• elementary school: 14 hours, middle school: 9 hours

• elementary school: 13 hours, middle school: 6 hours

• elementary school: 13 hours, middle school: 10 hours

• elementary school: 7 hours, middle school: 15 hours

Open Ended

These two box plots show the distances of a standing jump, in inches, for a random sample of 10-year-olds and a random sample of 15-year-olds. Is there a meaningful difference in median distance for the two populations? Explain how you know.

Open Ended

The median income for a sample of people from Chicago is about $$60,000$$ and the median income for a sample of people from Kansas City is about $$46,000$$ , but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.

Multiple Choice

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

• A sample of size 25 will produce more variability of the estimator than a sample of size 50.

• A sample of size 25 will produce less variability of the estimator than a sample of size 50.

• A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

• A sample of size 25 will produce a more biased estimator than a sample of size 50.

• A sample of size 25 will produce a less biased estimator than a sample of size 50.

Multiple Choice

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. (The sample proportion is 15/50 or .3) What is the probability of getting a sample of size 50 that has 15 or more students who believe Monday will be a snow day?

• 0.376

• Cannot be determined because the distribution of the sample proportion of samples of size 50 is not normal

• 0.624

• 0.99999

Multiple Choice

At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

•  78% is a population and 72% is a sample.
• 72% is a population and 78% is a sample
• 78% is a parameter and 72% is a statistic
• 72% is a parameter and 78% is a statistic

Multiple Choice

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 10% of 180 is > 10

• The sampling distribution is normal because np and nq are both > 10