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 41 22 31 94 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. Ho: There is no association between Star Trek fatalities and uniform color. Ha There is an association between Star Trek fatalities and uniform color. b. Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to 1 decimal place). Blue Dead Total 8 49 6 28 25 56 39 133 Gold Red = P-value= Alive c. Use appropriate technology to compute the value of the test statistic (rounded to 2 decimal places) and the P-value (rounded to 3 decimal places). x² Dead
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 41 22 31 94 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. Ho: There is no association between Star Trek fatalities and uniform color. Ha There is an association between Star Trek fatalities and uniform color. b. Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to 1 decimal place). Blue Dead Total 8 49 6 28 25 56 39 133 Gold Red = P-value= Alive c. Use appropriate technology to compute the value of the test statistic (rounded to 2 decimal places) and the P-value (rounded to 3 decimal places). x² Dead
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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 are 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 \( \alpha = 0.05 \) to test to see if a crew-member's fatality onscreen is dependent on their uniform color.
### Observed Counts
| | Alive | Dead | Total |
|----------|-------|------|-------|
| Blue | 41 | 8 | 49 |
| Gold | 22 | 6 | 28 |
| Red | 31 | 25 | 56 |
| **Total**| 94 | 39 | 133 |
#### a. Choose the correct null and alternative hypotheses.
- \( H_0 \): There is no association between Star Trek fatalities and uniform color.
- \( H_a \): There is an association between Star Trek fatalities and uniform color.
*(The first set of hypotheses is correctly chosen.)*
#### b. Complete the following table of expected counts under the assumption that the null hypothesis is true. (Round your answers to 1 decimal place).
| | Alive | Dead |
|----------|-------|------|
| Blue | | |
| Gold | | |
| Red | | |
#### c. Use appropriate technology to compute the value of the test statistic (rounded to 2 decimal places) and the \( \chi^2 \) and the \( P \)-value (rounded to 3 decimal places).
\( \chi^2 = \)
\( P \)-value =
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