Sampling Variability and Proportions

In this lesson, Mr. Holcomb explores the concept of variability in estimating a population proportion. The lesson involves a classroom activity where students build a distribution of sample proportions using colored cubes. The variability in sample proportions is analyzed, and the effect of increasing sample size on variability is discussed. The lesson concludes with a comparison of sampling distributions for different sample sizes, highlighting the decrease in variability with larger samples.

What is the main focus of lesson 19?

• Understanding variability in estimating a population proportion

• Learning about geometric shapes

• Exploring algebraic equations

• Studying historical events

In the sample proportion activity, what is used to represent the population?

• Colored cubes

• Coins

• Dice

• Number cards

How is the sample proportion calculated in the activity?

• By subtracting the number of yellow cubes from the total

• By multiplying the number of green cubes by the total number of cubes

• By adding the number of red and blue cubes

• By dividing the number of red cubes by the total number of cubes

What happens to the variability in the distribution as the sample size increases?

• It increases

• It becomes unpredictable

• It decreases

• It remains the same

What shape does the distribution take when the sample size is increased?

• Random

• Exponential

• Linear

• Bell-shaped curve

What is the shape of the distribution when the sample size is 10?

• Spread out with no clear shape

• Bell-shaped

• Linear

• Exponential

What is the effect of increasing the sample size to 30 on the sampling distribution?

• The distribution becomes more centered and symmetrical

• The distribution becomes more scattered

• The distribution becomes less predictable

• The distribution remains unchanged

How confident can we be in our estimate of the population proportion with a larger sample size?

• Less confident due to increased variability

• More confident due to reduced variability

• Not confident at all

• Equally confident regardless of sample size

What is the expected outcome if the sample size is increased to 50?

• The sampling variability will increase

• The sampling variability will decrease further

• The sampling variability will become unpredictable

• The sampling variability will remain the same

What is the main conclusion about sampling variability from the lesson?

• Larger sample sizes lead to less variability

• Variability increases with larger samples

• Smaller sample sizes are more accurate

• Variability is unaffected by sample size