Sampling to Draw Inferences

There are 15 circles in the population.

20% of the circles are red.

The best representative sample would also have 20% red circles.

It is RARE for your sample to be EXACTLY the same. We hope the sample is SIMILAR or CLOSE.

In a sample of 3 each circle is 33% (so not 20%). Which sample is the MOST representative of the population?

Which is the BEST sample of the 4 random samples?

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Answer explanation

The population is MOSTLY purple and SOME red.

This is the only sample that is MOSTLY purple and some red.

This is the MOST representative sample even though it is not exactly the same as the population.

Another word for a "smaller group"

is

SUBSET

Your sample is a subset of the population.

Which answer describes a sample?

• A sample is a SUBSET selected from the population

• A sample is the entire population

• A sample is a larger group than the population

BEWARE: Your sample does not allow for someone in China to be represented.

If you survey students in your town then your population is limited to students in your town.

What makes a sample representative?

• The sample is representative if it includes people from all over the world

• The sample is representative if it includes people from the same town

• The sample is representative if it includes people from the same country

• The sample is representative if it accurately reflects the group it is supposed to represent

When taking a sample You want to choose individuals/objects FROM THE POPULATION Anyone in the population could potentially be part of the sample is ideal. Which below is the best way to take a sample?

• Only select individuals who are easily accessible

• Select individuals based on personal bias

• Select individuals randomly from the entire population

• Only select individuals who respond to a public survey

In an effort to try to convince her mother that she is too old to join the intermediate swim​ class, Mira, who is 13 years​ old, gathers data on the ages of a random sample of members of the current intermediate swim class. The results of the data collected by Mira are displayed in the dot plot shown.

• It is likely that she will be able to convince her mother.​ Mira's age is within the area where the data are clustered.

• It is likely that she will be able to convince her mother.​ Mira's age is to the left of the area where the data are clustered.

• It is unlikely that she will be able to convince her mother.​ Mira's age is within the area where the data are clustered.

• It is unlikely that she will be able to convince her mother.​ Mira's age is to the left of the area where the data are clustered.

The following dot plots show the amount of time it takes each​ person, in a random​ sample, to complete two similar problems. Make a comparative inference about the two problems.

• The problems are equally challenging.

• Problem 2 is more difficult because it took students longer on average.

• Problem 1 is more difficult because it took students longer on average.

The following shows the number of calls two radio shows get each day for a ten day period. The two shows are on at the same time. Make a comparative inference based on the median values.

• Show 1 usually receives more calls.

• Show 2 usually receives more calls.

• The shows usually receive equal numbers of calls.

• There is not enough data to draw an inference.

A random survey of 7th graders finds that 7 out of 10 have more than 1 hour of screen time each day. If there are 110 7th graders in your school, how many would you expect to have more than 1 hour of screen time?

• 77

• 70

• 75

• 81

A valid sample shows that 3 of 20 players win at a carnival game. If 275 people play the game each day, how many winners would you expect to have?

• about 50

• about 45

• about 41

• about 36

3 of 5 doctors surveyed by a pharmaceutical company prefer their new Brand X medicine compared to the other leading brand. Is this a valid inference?

• Yes they randomly chose doctors for the survey.

• No there is no evidence that they chose the doctors for the survey at random.

• Yes they chose doctors they knew would prefer their Brand X.

• No they randomly chose doctors for the survey.