In this activity, you are going to take a random sample from an actual population (of your choice), gather data from your sample, calculate sample statistics, and then calculate standard errors to decide how accurate the sample statistics are likely to be.

Step 1:

Decide on a population of at least 15 well known people. The population can be whatever you like as long as it is possible to gather data about the population members from public websites. Some possible options are the former US presidents, singers who have sold over 10 million albums, SF Giants players, and current US governors.

Step 2:

Give each population member an ID number from 1 to N. In other words, if your population has 30 people, number the population members from 1 to 30. If your population has 40 people, number the population members from 1 to 40. It is up to you to decide how to number the population members. If you like, you can use a systematic approach (like starting at the youngest population member and moving up to the oldest population member), but you could also just decide what number you would like to assign to each population member as long as the numbers go from 1 to N.

Step 3:

Go to random.org and use the random number generator to randomly select 10 people from your population. You will need to enter 1 for the minimum, the number of population members for the maximum (whatever it happens to be), and click on Generate 10 times. Write down the numbers that you generate. If you get the same number twice, just ignore it and click Generate again.

Step 4:

Answer the following questions and show your work when it is requested.

1. What is the name of your chosen population?

2. In the columns that are provided, write the names of the population members (all of them, not just the ones that you selected) and the ID number you assigned to each population member

Population Member ID number

3. Write out the numbers that you randomly generated with random.org. Separate the numbers with commas.

(Note: It is important to select a random sample. If it isn't random, then the standard error will be meaningless).

4. Write out the name of a quantitative variable that you could record from each member of your sample. It can be age, height, number of children, or something else.

5. Record the variable you mentioned in Question 4 for all people in your sample. After collecting the data, fill in the two columns below. In the first column, write the names of the people in your sample. In the second column, write each person's data value.

Person Data Value

6. Calculate the mean of your sample (by adding the 10 data values and dividing by 10).

Show at least some work and round your answer to 2 decimal places. Make sure to calculate the mean of the data values, not the mean of the ID numbers that you generated with random.org.

7. Calculate the standard deviation of your sample. Round your answer to two decimal places.

8. Calculate the estimated standard error of your sample mean using a regular calculator. Show at least some work and round your answer to two decimal places.

9. What is the standard error telling you?

10. Write the name of a qualitative variable that you could record from each person in your sample. It could be gender, ethnicity, marital status, or something else.

11. Record the variable you mentioned in Question 10 for all members of your sample and write each person's data value in the column below.

Data Value

12. Use the data to calculate the proportion of something in your sample. After you do the calculations, fill in the two blanks to complete the sentence.

I calculated the proportion of ____________ in my sample. It came out to ____________

(rounded to 2 decimal places)

Note: The sample proportion needs to be written as a decimal, not as a percentage.

For example, if your sample proportion is 0.17, then write 0.17 instead of 17%

13. Calculate the estimated standard error of your sample proportion using a calculator. Round your answer to 2 decimal places. Show at least some work.

14. What is the standard error telling you?