Question

statistics and probability
generating random samples from a population with known characteristics
construct a percent bar graph for the mixed nuts in the container.
lets simulate three random samples of 200 mixed nuts from the container. press all three
un\ buttons to do so. (you can press
un\ multiple times to generate more samples to see how they vary.)
(b) in part (a), we calculated two different types of percentages: population percentages in the percent bar graph and sample percentages in the simulations.

• the almond population percentage is the percentage of the 7000 mixed nuts that are almonds.
• the almond sample percentage is the percentage of mixed nuts that are almonds in a random sample of 200 mixed nuts.

true or false?

Explanation:

• First statement: In sampling, there is sampling variability. A sample percentage (like almond sample percentage) is an estimate of the population percentage (almond population percentage). Due to randomness in sampling, the sample percentage is not always equal to the population percentage.
• Second statement: The population percentage of almonds is \(50\%\) (from the bar - graph). But because of sampling variability (random selection of nuts in the sample), the sample percentage of almonds in a sample of size \(n = 200\) is not always \(50\%\). It is an estimate that can vary around \(50\%\).
• Third statement: While a very large sample size reduces the sampling error (the difference between the sample percentage and the population percentage), it does not completely eliminate it. There is always a non - zero probability (however small for large samples) of some difference due to random sampling.

Answer:

1. False
2. False
3. False