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 $\displaystyle \alpha$ = 0.05 to test to see if a crew-member's fatality onscreen is dependent on their uniform color.

	Alive	Dead	Total
Blue	41	10	51
Gold	18	9	27
Red	29	24	53
Total	88	43	131

1. Choose the correct null and alternative hypotheses.
   • $\displaystyle {H}_{{0}}:$ There is no association between Star Trek fatalities and uniform color.
     $\displaystyle {H}_{{a}}$ There is an association between Star Trek fatalities and uniform color.
   • $\displaystyle {H}_{{0}}:$ There is an association between Star Trek fatalities and uniform color.
     $\displaystyle {H}_{{a}}$ There is no association between Star Trek fatalities and uniform color.
   
   
   
2. Compute the test statistic.
   
   Complete the following table of expected counts. (Round your answers to 4 decimal places).
   
   

   	Alive	Dead
   Blue
   Gold
   Red

   
   Compute the value of the test statistic. (Round your answer to 4 decimal places.)
   
   $\displaystyle \chi^{{2}}=$
   
   
3. Compute the p-value. (Round your answer to 4 decimal places.)
   
   $\displaystyle {p}$-value =
   
   
4. 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.
   • The p-value provides little evidence against the null hypothesis. The association between Star Trek fatalities and uniform color is not statistically significant.