The mean hatching time for group 1 is 25.8 days, and the mean hatching time for group 2 is 25.2 days.

1. How could the biologist get a randomization distribution to compare the two groups?
2. How would the biologist use the randomization distribution to determine whether the difference between the mean hatching time for group 1 and the mean hatching time for group 2 is due to chance?

Technology required

Diego rolls a standard number cube 10 times and adds the values to get a sum of 40. Is that unusually high? Priya simulates rolling the number cube 10 times on a computer and adds the values. She repeats that process 100 times and creates a histogram of the results.

1. Based on the histogram, does 40 seem unusually high? Explain your reasoning.
2. The mean of Priya’s simulations is a sum of 35, and the standard deviation is 5.72. Using a normal distribution as an approximation of this distribution, what is the probability that a person would roll a sum greater than 40?

Why do we use randomization distributions?

Which of these values would be most useful for determining whether the difference in means is likely due to the treatment? Explain your reasoning.

1. interquartile range
2. median
3. standard deviation
4. range

A distribution is approximately normal with a mean of 70 and a standard deviation of 10. Match the interval with the approximate percentage of data that falls within that interval.