Lesson 17: More About Sampling Variability | Unit 8: Probability and Sampling

Open Ended

A marketing company wants to know how far baseball fans are willing to travel to watch a game. They select 100 different samples, each of size 40, from different parts of the country. Here is a dot plot showing the mean of each sample. Based on the distribution of sample means, what do you think is a reasonable estimate for the mean of the population?

Multiple Choice

Does the number of dots on the dot plot tell us how many people were at the concert or how many students are in the math class?

• How many people were at the concert

• How many students are in the math class

Open Ended

The mean age for the population is 35 years. If Elena picks a new sample of size 10 from this population, should she expect her sample mean to be within 1 year of the population mean? Explain your reasoning.

Multiple Choice

What could Elena do to select a random sample that is more likely to have a sample mean within 1 year of the population mean?

• Increase the sample size and use stratified sampling.
• Decrease the sample size and use random sampling.
• Use a biased sample from a specific age group.
• Select only the oldest individuals in the population.

Multiple Choice

A farmer grows 5,000 pumpkins each year. The pumpkins are priced according to their weight, so the farmer would like to estimate the mean weight of the pumpkins he grew this year. He randomly selects 8 pumpkins and weighs them. Here are the weights (in pounds) of these pumpkins: 2.9, 6.8, 7.3, 7.7, 8.9, 10.6, 12.3, 15.3. What is the mean weight of the pumpkins the farmer grew?

• 10.0
• 7.5
• 8.975
• 9.2

Multiple Choice

A farmer grows 5,000 pumpkins each year. This dot plot shows the mean weight of 100 samples of 8 pumpkins, similar to the sample above. What appears to be the mean weight of the 5,000 pumpkins?

• 7 pounds
• 10 pounds
• 12 pounds
• 9 pounds

Multiple Choice

A farmer grows 5,000 pumpkins each year. This dot plot shows the mean weight of 100 samples of 8 pumpkins, similar to the sample above. What does the dot plot of the sample means suggest about how accurate an estimate based on a single sample of 8 pumpkins might be?

• Estimates based on a single sample of 8 pumpkins may not be accurate due to variability in sample means.
• Estimates based on a single sample are always accurate.
• Variability in sample means is negligible for small samples.
• A single sample of 8 pumpkins provides a perfect estimate.

Multiple Choice

A farmer grows 5,000 pumpkins each year. What do you think the farmer might do to get a more accurate estimate of the population mean?

• Count all the pumpkins individually to find the mean.
• Estimate the mean based on last year's yield.
• Use the average weight of pumpkins to calculate the mean.
• Take a random sample of pumpkins to estimate the population mean.