Sampling Variability and Sample Means

Mrs. Zia's lesson on sampling variability explores the significance of differences between sample means. Students engage in activities using bags of numbers to understand how sample means can vary due to random sampling. The lesson emphasizes the importance of considering sampling variability when comparing population means. Through exercises, students learn to analyze dot plots and predict population means based on sample data.

Why is it important to consider sampling variability when comparing two sample means?

• It helps in understanding the true difference between population means.

• It guarantees that the sample means are equal.

• It ensures that the samples are identical.

• It eliminates any errors in data collection.

What is the first step in investigating the population mean of numbers in a bag?

• Create a histogram of the numbers.

• Compare the sample with another bag.

• Calculate the mean of all numbers.

• Select a random sample of 10 numbers.

How can you estimate the mean of numbers in a sample?

• By looking at the center of the data in a dot plot.

• By counting the total numbers in the sample.

• By comparing it with another sample.

• By checking the range of the numbers.

What does it mean if two dot plots have similar centers?

• The samples are identical.

• The samples have the same range.

• The sample means are different.

• The sample means are likely to be similar.

Why might the sample means of different students vary?

• Due to sampling variability.

• Because of errors in calculation.

• Because the samples are identical.

• Due to incorrect data entry.

What can be concluded if the difference between two sample means is close to zero?

• The population means might be similar.

• The samples have the same range.

• The samples are identical.

• The population means are different.

How can you be sure which bag has the larger population mean?

• By ensuring the samples are identical.

• You cannot be sure due to sampling variability.

• By comparing the sample means directly.

• By checking the range of numbers.

What is a meaningful difference between two sample means?

• One that is less than one.

• One that is exactly zero.

• One that is unlikely to have occurred by chance.

• One that is greater than ten.

What does a class dot plot of differences in sample means show?

• The variability in sample means.

• The exact population means.

• The identical nature of samples.

• The errors in data collection.

What should be considered when making decisions based on sample means?

• The exact value of each sample mean.

• The distribution of the difference in sample means.

• The identical nature of the samples.

• The range of numbers in each sample.