To answer part (a), we need to outline a completely randomized design for this experiment. Based on the information provided, the steps would be as follows:

1. Start with 20 cups of popcorn (10 cups for soaking and 10 cups for no soaking).
2. Randomly assign 10 cups to the soaked group and 10 cups to the unsoaked group. This random assignment ensures no bias.
3. The soaked group will soak the kernels in water before popping.
4. The unsoaked group will pop kernels without soaking them.
5. After popping, compare the percentage of kernels that popped in each group.

Now, for part (b), let's calculate the mean percentage of popped kernels for each group:

Soaked Group:

The percentages for the soaked group are: 83, 91, 88, 86, 96, 97, 94, 92, 86, 93.

To calculate the mean: $\text{Mean (soaked)} = \frac{83 + 91 + 88 + 86 + 96 + 97 + 94 + 92 + 86 + 93}{10} = \frac{906}{10} = 90.6\%$

Unsoaked Group:

The percentages for the unsoaked group are: 89, 89, 81, 77, 84, 79, 82, 96, 91, 93.

To calculate the mean: $\text{Mean (unsoaked)} = \frac{89 + 89 + 81 + 77 + 84 + 79 + 82 + 96 + 91 + 93}{10} = \frac{862}{10} = 86.2\%$

Difference in Means:

$\text{Difference (soaked - unsoaked)} = 90.6\% - 86.2\% = 4.4\%$

Answers:

• The mean percentage of popped kernels for the soaked group is 90.6%.
• The mean percentage of popped kernels for the unsoaked group is 86.2%.
• The difference in mean percentage is 4.4%.

Let me know if you need further details or have any questions! Here are some related questions you might find interesting:

1. How would randomization help reduce bias in this experiment?
2. What other factors could affect the percentage of kernels that pop, aside from soaking?
3. Why is it important to have the same number of cups in each group?
4. How could you increase the precision of this experiment?
5. What would happen if the number of kernels in each cup was not kept the same?

Tip: Always ensure that randomization is applied to the assignment of treatments to avoid any confounding variables influencing the results.