Sampling Variability and Sample Means

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

What is the main focus of the lesson introduced by Mr. Holcomb?

• Sampling variability and the effect of sample sizes

• The history of mathematics

• Advanced calculus techniques

• Geometry and its applications

In the first dot plot, what is the range of the mean time people spent at the gym?

• 41 to 65 minutes

• 34 to 78 minutes

• 20 to 50 minutes

• 60 to 90 minutes

What is the purpose of using a table of random digits in the sampling process?

• To select random samples from the population

• To determine the population size

• To find the median of the data

• To calculate the mean directly

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

• 5 times

• 20 times

• 10 times

• 15 times

What is the calculated mean of the 15 sample values in the continuation of the sampling process?

• 50.2

• 54.9

• 60.0

• 48.1

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

• The size 5 plot is narrower

• The size 5 plot has more repeated values

• The size 15 plot is more clustered

• The size 15 plot is more spread out

What is the expected distance of the sample mean from the population mean for a sample size of 15?

• Approximately 1 to 2 minutes

• Approximately 5 to 6 minutes

• Approximately 2 to 3 minutes

• Approximately 10 to 12 minutes

What effect does increasing the sample size to 25 have on the sampling variability?

• It increases the variability

• It decreases the variability

• It has no effect on the variability

• It makes the variability unpredictable

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

• To reduce the time spent on sampling

• To make calculations easier

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

• To increase the range of the data

What is the actual population mean of the time spent at the gym?

• 50.2 minutes

• 53.9 minutes

• 48.1 minutes

• 60.0 minutes