Warm-Up p.930 Aug. 26th

Sampling from a Population

By Hand.•Finding the average or mean.

Sum of all the itemsThe total number of items

With Calculator.1. STATENTER2. Type all data in L1. 3. Then push STAT, scroll

over to CALC.4. Then click 1.5. Then push ENTER

multiple times until you see numbers.

Write your ten word sample in your spiral.Count and calculate the average.

What’s the average length of each word in

the Start Spangled Banner?

Create a Class Dot Plot With Average Number of Words

Randomness of Words Picked• The original Star Spangled Banner has 314 words.

• If you were truly completing this randomly…

• You would have someone pick 10 random numbers out of a hat for example

•Now lets find the average of those 10 numbers and see if it checks out.

Random Integers Using Technology•Press MATH, go over to PROB, then click 5. • There are multiple options (randInt, randIntNoRep)

•Enter your Lower, and Upper digits.• For us our Lower=1, and our Upper=314.

•N= how many random numbers desired.• For us this is 10.

•Then press ENTER.Now use this function and try one more time with your calculator.

Once you have your new words find the true average of word lengths.

Now Place Your New Values On the Bottom of the Dot Plot Line

Notice the differences.•The original study was biased because people eyes tend to be drawn to larger objects or words.

•So some of you may have chosen words simply because of we tend to pay attention to larger words and ignore the smaller ones.

Vocabulary•Population: is the entirety of whatever your studying…

(words, people, trees, etc.)

Hard to actually collect data on an entire population. (US Census)

• Sample: smaller subset of the population.

We can then use this information to make predictions for the entire population.

• Statistical Inference: is the process of using data from a sample to gain information about the population.

• Sampling bias: occurs when the method of selecting a sample causes the sample to differ from the population in some relevant way. If it exists then we cannot make assumptions about the entire population.

Ideally when sampling you want the sample to be identical to the entire population in every way only smaller in total size.

Star Spangled Banner Case1. What are the population and the sample in

the activity?

2. What are the cases?

3. What is the variable?

4. Is the variable quantitative or categorical?

Only truly random samples can be trusted when making generalizations about the population.

Task #2 Hours Spent Studying

Task #3 School Advisory Panel

There are many issues that can lead to sampling bias:1. Sampling units (people) based on something

clearly related to the variables you are studying.

2. Letting your sample be comprised of whoever chooses to participate (volunteer bias).

3. The way a question is asked may introduce bias.

4. Reponses are not anonymous.

•A student at East Mecklenburg sends out an email to all 1756 students asking students to reply whether or not they plan to go tot college after graduating high school. Of 1054 responding 19% said no. Can you conclude that about 81% of all students in your high school are planning to go to college? Why or why not? What are you considering as the sample, and what is the population? Is there any bias in the sampling method?

Biased?