IM 7.8.17 Lesson: More about Sampling Variability
The other day, you worked with the reaction times of twelfth graders to see if they were fast enough to help out at the track meet. Look back at the sample you collected.
Calculate the mean reaction time for your sample.
Did you and your partner get the same sample mean? Explain why or why not.
Plot your sample mean from the previous activity onto this dot plot.
What do you notice about the distribution of the sample means from the class?
The population mean is 0.442 seconds. How does this value compare to the sample means from the class?
Here is a dot plot of the population of reaction times.
What do you notice about the distribution of the population?
Compare the two displayed dot plots.
Based on the distribution of sample means from the class, do you think the mean of a random sample of 20 items is likely to be within 0.01 seconds of the actual population mean? Explain your reasoning.
Based on the distribution of sample means from the class, do you think the mean of a random sample of 20 items is likely to be within 0.1 seconds of the actual population mean? Explain your reasoning.
The other day you worked with 2 different samples of viewers from each of 3 different television shows. Each sample included 10 viewers. Here are the mean ages for 100 different samples of viewers from each show.
For Trivia the Game Show, use the dot plot to estimate the population mean.
For Science Experiments YOU Can Do, use the dot plot to estimate the population mean.
For the Learning to Read show, use the dot plot to estimate the population mean.
For each show, are most of the sample means within 1 year of your estimated population mean?
Suppose you take a new random sample of 10 viewers for each of the 3 shows. Which show do you expect to have the new sample mean closest to the population mean? Explain or show your reasoning.
Market research shows that advertisements for retirement plans appeal to people between the ages of 40 and 55. Younger people are usually not interested and older people often already have a plan. Is it a good idea to advertise retirement plans during any of these three shows? Explain your reasoning.