The dot plot displays a randomization distribution of 325 simulations redistributing data from an experiment.

Select all of the values that represent a difference of the means in which there is evidence to determine that the results are likely due to the treatment.

Technology required

Here are the mean amounts of milk, in gallons, produced weekly by 12 random samples with 20 dairy cows in each sample.

• 64.5
• 62.7
• 63.5
• 65.0
• 64.1
• 62.7
• 62.4
• 63.5
• 60.7
• 61.6
• 63.0
• 65.6

Use the values to estimate the mean amount of milk produced weekly by the dairy cow population, and provide a margin of error.

An internet company uses a random sample of 200 internet users and simulations to estimate the proportion of people who stream videos. The company estimates the proportion is 0.855 with a margin of error of 0.081. They decide to check their results by collecting another random sample with 300 internet users. Which of the results is most likely to be the estimates from the second random sample and simulations?

Mai has a box of standard number cubes. After rolling a number cube 20 times, she notices that the number 4 appears 9 times.

Mai suspects that this number cube is weighted in some way to make 4 appear more often than the other numbers. Mai has another number cube from the box that she has confirmed is fair (all of the numbers tend to be rolled with equal frequency). Explain a process in which Mai could use the fair number cube to gather evidence to show whether the number cube used in the original rolls is unfair.