compare the minimal expe selected. Minimal 1 Substantial 1: What would be O Ho: ud = 0 O Ho: Identical F O Ha: p1-p2-0 O Ho: Identical Sa

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what would be the null hypothesis for the permutation test?
### Comparing Word Puzzle Completion Times

#### Research Overview
A researcher aimed to compare the times required to complete a word puzzle based on participants' levels of experience with video games. The study categorized participants into two groups: those with minimal experience and those with substantial experience. Participants were randomly selected for the experiment.

#### Data
The time taken (in minutes) by participants from each group to complete the puzzle is presented in the table below:

| Minimal Experience | Substantial Experience |
|--------------------|------------------------|
| 17                 | 12                     |
| 18                 | 13                     |
| 17                 | 14                     |
| 19                 | 15                     |
| 17                 | 18                     |
| 16                 | 100                    |
| 14                 | 17                     |
| 14                 | 14                     |

#### Null Hypothesis
The null hypothesis for this two-sample t-test would be:
- \( H_0: \mu_d = 0 \) (No difference in the population means of the two groups)

##### Other Hypotheses Options:
- \( H_0: p_1 - p_2 = 0 \)
- \( H_0: \) Identical Population Distributions
- \( H_0: \) Identical Sample Distributions

### Graph Explanation
If there were any graphs or diagrams present, they would typically show a visual comparison of the completion times between the two groups, possibly including:
- **Box Plots:** To display the distribution of completion times within each experience level.
- **Histograms:** To show the frequency of completion times across different intervals for each group.
- **Scatter Plots:** To visualize any potential correlation between experience level and completion time.

By comparing the provided data and visual aids, researchers can observe trends and differences in performance between the two categories of participants, ultimately testing the null hypothesis to determine if video game experience significantly affects puzzle completion time.
Transcribed Image Text:### Comparing Word Puzzle Completion Times #### Research Overview A researcher aimed to compare the times required to complete a word puzzle based on participants' levels of experience with video games. The study categorized participants into two groups: those with minimal experience and those with substantial experience. Participants were randomly selected for the experiment. #### Data The time taken (in minutes) by participants from each group to complete the puzzle is presented in the table below: | Minimal Experience | Substantial Experience | |--------------------|------------------------| | 17 | 12 | | 18 | 13 | | 17 | 14 | | 19 | 15 | | 17 | 18 | | 16 | 100 | | 14 | 17 | | 14 | 14 | #### Null Hypothesis The null hypothesis for this two-sample t-test would be: - \( H_0: \mu_d = 0 \) (No difference in the population means of the two groups) ##### Other Hypotheses Options: - \( H_0: p_1 - p_2 = 0 \) - \( H_0: \) Identical Population Distributions - \( H_0: \) Identical Sample Distributions ### Graph Explanation If there were any graphs or diagrams present, they would typically show a visual comparison of the completion times between the two groups, possibly including: - **Box Plots:** To display the distribution of completion times within each experience level. - **Histograms:** To show the frequency of completion times across different intervals for each group. - **Scatter Plots:** To visualize any potential correlation between experience level and completion time. By comparing the provided data and visual aids, researchers can observe trends and differences in performance between the two categories of participants, ultimately testing the null hypothesis to determine if video game experience significantly affects puzzle completion time.
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