Sampling Variability and Sample Means

The video lesson covers sampling variability and the effect of sample sizes on statistical analysis. It includes classwork examples and exercises that guide students through selecting random samples, calculating sample means, and creating dot plots. The lesson emphasizes the importance of sample size in reducing variability and improving the accuracy of statistical estimates.

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

• Means of 20 samples with 5 data points each

• Means of 15 samples with 20 data points each

• Means of 5 samples with 20 data points each

• Means of 20 samples with 15 data points each

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

• It uses fewer data points per sample

• The sample means are more tightly clustered

• It shows more variability in sample means

• It has a wider range of sample means

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

• Choose a random number between 1 and 100

• Select a three-digit number from the table

• Calculate the mean of the sample

• Estimate the population mean

How many times should the random sampling process be repeated to calculate the sample mean?

• 20 times

• 15 times

• 10 times

• 5 times

What is the purpose of calculating the mean of 15 sample values?

• To determine the mode of the sample

• To estimate the population mean

• To find the median of the population

• To calculate the range of the sample

How does the dot plot of sample means from samples of size 15 compare to that of size 5?

• It is more clustered and shows less variability

• It has a wider range

• It is more spread out

• It has no repeated values

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

• It is less likely to be close to the population mean

• It is more likely to be close to the population mean

• It has a wider range of values

• It is more spread out

What is the expected benefit of using a sample size of 25?

• Closer approximation to the population mean

• Increased sampling variability

• Wider range of sample means

• Less confidence in the results

How far can a statistician expect the sample mean to be from the population mean with a sample size of 25?

• Approximately 5 to 6 minutes

• Approximately 10 minutes

• Approximately 3 to 4 minutes

• Approximately 15 minutes

Why is it preferable to choose a larger sample size?

• It increases the sampling variability

• It results in a wider range of sample means

• It decreases the confidence in the sample mean

• It makes the sample mean closer to the population mean