Sampling Variability and Sample Size

This video tutorial by Mr. Holcomb covers lesson 18 on sampling variability and the effect of sample sizes. It includes classwork examples and exercises that demonstrate how to select random samples, calculate sample means, and create dot plots. The lesson emphasizes the importance of sample size in reducing sampling variability and provides practical exercises to illustrate these concepts.

What does the first dot plot represent in the context of sampling variability?

• Means of 20 samples with 5 data points each

• Means of 20 samples with 15 data points each

• Means of 5 samples with 20 data points each

• Means of 15 samples with 20 data points each

Why is the second dot plot considered more reliable for answering the statistical question?

• It includes more data points

• The sample means are more tightly clustered

• It has a larger range of values

• It shows a greater variability

What is the first step in selecting a random sample from a population using a table of random digits?

• Estimate the population mean

• Calculate the mean of the sample

• Select a three-digit number from the table

• Choose a random number between 1 and 100

How many times should the process of selecting a random sample be repeated to calculate the sample mean?

• 5 times

• 10 times

• 20 times

• 15 times

What is the purpose of creating a dot plot for the class data?

• To determine the mode of the data

• To calculate the median of the data

• To visualize the distribution of sample means

• To compare individual data points

Which sample size shows greater sampling variability, 5 or 15?

• Neither shows variability

• Sample size 5

• Sample size 15

• Both have equal variability

What does a smaller sampling variability indicate about the sample mean?

• It is less reliable

• It is closer to the population mean

• It is more spread out

• It is less clustered

How does increasing the sample size to 25 affect the sampling variability?

• It has no effect on variability

• It makes the variability unpredictable

• It decreases the variability

• It increases the variability

What is the expected distance of the sample mean from the population mean when using a sample size of 25?

• Approximately 15 minutes

• Approximately 10 minutes

• Approximately 5 minutes

• Approximately 3 to 4 minutes

Why is it preferable to choose a sample size that minimizes sampling variability?

• To increase the range of data

• To ensure the sample mean is closer to the population mean

• To make calculations easier

• To reduce the number of samples needed