The color of the Star Trek uniform represents each crew-member's work area. In the original Star Trek series, blue shirts are worn by medical and science staff, gold shirts are worn by the command division, and the red shirts were worn by engineering, security and communications division. We will statistically assess whether there is a connection between uniform color and the fatality rate. The table below shows a sample of how many crew-members in each area have died onscreen and their shirt color. Use a = 0.05 to test to see if a crew-member's fatality onscreen is dependent on their uniform color. Blue Gold Red Total Alive 38 20 31 89 a. Choose the correct null and alternative hypotheses. O Ho: There is an association between Star Trek fatalities and uniform color. Ha There is no association between Star Trek fatalities and uniform color. O Ho: There is no association between Star Trek fatalities and uniform color. Ha There is an association between Star Trek fatalities and uniform color. Blue Dead 9 7 24 40 b. Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to 1 decimal place). Gold Total 47 27 55 129 Red P-value= Alive Dead c. Use appropriate technology to compute the value of test statistic (rounded to 2 decimal places) and the P-value (rounded to 3 decimal places). d. Interpret the results of the significance test. O The P-value provides strong evidence against the null hypothesis. The association between Star Trek fatalities and uniform color is statistically significant. O The P-value provides little evidence against the null hypothesis. The association between Star Trek fatalities and uniform color is not statistically significant.

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### Exploring the Relationship Between Uniform Color and Fatality Rate on Star Trek

The color of the Star Trek uniform represents each crew member's work area. In the original Star Trek series, blue shirts are worn by medical and science staff, gold shirts are worn by the command division, and red shirts are worn by engineering, security, and communications divisions. We aim to statistically assess whether there is a connection between uniform color and the fatality rate. 

Below is a table showing a sample of how many crew members in each area have died onscreen and their shirt color. We will use a significance level (α) of 0.05 to test if a crew member's fatality onscreen is dependent on their uniform color.

**Uniform Color and Fate Onscreen:**

| Color | Alive | Dead | Total |
|-------|-------|------|-------|
| Blue  | 38    | 9    | 47    |
| Gold  | 20    | 7    | 27    |
| Red   | 31    | 24   | 55    |
| **Total** | **89** | **40** | **129** |

**Steps to Follow:**

#### a. Choose the Correct Null and Alternative Hypotheses:
1. \( H_0 \): There is no association between Star Trek fatalities and uniform color.
2. \( H_a \): There is an association between Star Trek fatalities and uniform color.

OR

1. \( H_0 \): There is no association between Star Trek fatalities and uniform color.
2. \( H_a \): There is an association between Star Trek fatalities and uniform color.

#### b. Calculate the Expected Counts:
Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to one decimal place.)

| Color | Alive | Dead |
|-------|-------|------|
| Blue  |       |      |
| Gold  |       |      |
| Red   |       |      |

#### c. Compute the Test Statistic:
Use appropriate technology to compute the value of the test statistic (rounded to two decimal places) and the P-value (rounded to three decimal places).

- Test Statistic (χ²) = 
- P-value = 

#### d. Interpret the Results of the Significance Test:
- The P-value provides strong evidence against the null hypothesis. The association between Star Trek fatalities and uniform color is **statistically significant**.
Transcribed Image Text:### Exploring the Relationship Between Uniform Color and Fatality Rate on Star Trek The color of the Star Trek uniform represents each crew member's work area. In the original Star Trek series, blue shirts are worn by medical and science staff, gold shirts are worn by the command division, and red shirts are worn by engineering, security, and communications divisions. We aim to statistically assess whether there is a connection between uniform color and the fatality rate. Below is a table showing a sample of how many crew members in each area have died onscreen and their shirt color. We will use a significance level (α) of 0.05 to test if a crew member's fatality onscreen is dependent on their uniform color. **Uniform Color and Fate Onscreen:** | Color | Alive | Dead | Total | |-------|-------|------|-------| | Blue | 38 | 9 | 47 | | Gold | 20 | 7 | 27 | | Red | 31 | 24 | 55 | | **Total** | **89** | **40** | **129** | **Steps to Follow:** #### a. Choose the Correct Null and Alternative Hypotheses: 1. \( H_0 \): There is no association between Star Trek fatalities and uniform color. 2. \( H_a \): There is an association between Star Trek fatalities and uniform color. OR 1. \( H_0 \): There is no association between Star Trek fatalities and uniform color. 2. \( H_a \): There is an association between Star Trek fatalities and uniform color. #### b. Calculate the Expected Counts: Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to one decimal place.) | Color | Alive | Dead | |-------|-------|------| | Blue | | | | Gold | | | | Red | | | #### c. Compute the Test Statistic: Use appropriate technology to compute the value of the test statistic (rounded to two decimal places) and the P-value (rounded to three decimal places). - Test Statistic (χ²) = - P-value = #### d. Interpret the Results of the Significance Test: - The P-value provides strong evidence against the null hypothesis. The association between Star Trek fatalities and uniform color is **statistically significant**.
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