## Problem 1: Reaction Time Analysis

### Problem Description:

The Jamovi assignment involves analyzing reaction time data from 20 participants using jamovi. The tasks include creating a jamovi spreadsheet, calculating z-scores, and answering specific questions based on the results.

Participant ID# |
Reaction Time (ms) |
---|---|

101 | 416 |

102 | 332 |

103 | 375 |

104 | 470 |

105 | 421 |

106 | 341 |

107 | 1262 |

108 | 359 |

109 | 396 |

110 | 392 |

111 | 431 |

112 | 464 |

113 | 496 |

114 | 438 |

115 | 493 |

116 | 1015 |

117 | 440 |

118 | 375 |

119 | 460 |

120 | 472 |

**Table 1: Jamovi spreadsheet for participant ID and Reaction time**

**Solution: **To analyze the data, a jamovi spreadsheet was created, and z-scores for reaction times were calculated. The following are the results:

**a) Participant Closest to Mean:
**

- Answer: Participant 115 had a reaction time closest to the sample mean, with a z-score of 0.003.

**b) Participants within ±0.5 Standard Deviations:
**

**Answer:**14 participants had reaction times within ±0.5 standard deviations of the sample mean.

**c) Identifying Outliers:
**

**Answer:**Participant 107, with a z-score of 3.351, would be removed as an outlier.

## Problem 2: PE Class Jumping Distance

### Problem Description:

Students' jumping distances at the beginning and end of the semester are analyzed. Questions involve hypothesis testing and result interpretation.

Student ID | First Week | Last Week |
---|---|---|

001 | 3 | 5 |

002 | 4 | 3 |

003 | 4 | 4 |

004 | 2 | 4 |

005 | 3 | 4 |

006 | 3 | 5 |

007 | 2 | 4 |

008 | 4 | 5 |

009 | 2 | 5 |

010 | 3 | 3 |

**Table 2: A weekly testing for student’s jumping distance**

**Solution:**

**a) Rejecting Null Hypothesis:
**

**Answer:**The null hypothesis of no change would be rejected as the difference in jumping distance is statistically significant at the 5% level.

**b) Results Statement:
**

**Answer:**A paired sample t-test showed significant improvement (t(9) = 3.1, p = .01, d = 0.2) in jumping distance over the semester.

**c) Plain Explanation:
**

**Answer:**On average, students jumped significantly farther in the last week compared to the first week, indicating improvement.

## Problem 3:Dark Chocolate and Diet

### Problem Description:

The effects of dark chocolate on a diet plan are investigated using an independent sample t-test.

Diet | Diet + Chocolate |
---|---|

2 | 3 |

3 | 3 |

2 | 5 |

4 | 4 |

3 | 2 |

3 | 3 |

2 | 4 |

4 | 4 |

1 | 3 |

2 | 2 |

**Table 3: The number of pounds each group lost at the end of the study.**

**Solution: **

**a) Rejecting Null Hypothesis:
**

**Answer:**The null hypothesis is not rejected as the difference in weight loss is not significant (p = .1).

**b) Results Statement:
**

**Answer:**The t-test result (t = -1.6, p = .12, d = -0.7) indicates no significant effect of dark chocolate on weight loss.

**c) Simple Explanation:
**

**Answer:**Dark chocolate did not significantly impact weight loss; both groups showed similar results.

## Problem 4: Journal Article Analysis

**Selected Article:** a) [Brustkern, J., Heinrichs, M., Walker, M. et al. Facial threat affects trust more strongly than facial attractiveness in women than it does in men. Sci Rep 11, 22475 (2021).

**b) Description:
**

**Answer:**The study explores the sex-specific effects of facial attractiveness and threat on trust. The t-test (t(91) = 1.415, p = 0.161) found no significant differences.

**c) Appropriateness of T-Test:
**

**Answer:**An independent samples t-test was appropriate for comparing two independent groups (men and women).

**d) Assumptions:
**

**Answer:**The paper did not explicitly report the test of normal distribution.

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