Question

raceethnicity	COUNTA of raceethnicity
Arab-American	3
Asian/Pacific Islander	21
Black	266
Hispanic/Latino	183
Native American	24
Unknown	22
White	574
Grand Total	1093

1. Perform a hypothesis test to examine the claim that the proportion of Hispanic/Latino people killed by police in the US is different from 16.4% (the 2014 demographic percentage for Hispanic/Latino Americans in the US population).

   1. Clearly state the null and alternative hypotheses to test, both as sentences and using symbols.

   2. Are the conditions (independent data and large enough sample size) met?

   3. Use technology to calculate the test statistic and the P-value.

   4. Make a sketch showing the distribution and the P-value.

   5. Using significance level 0.05, do you reject the null hypothesis or not?

   6. Communicate the conclusion of your hypothesis test in context.

      2. ​​​​​​​​​​​​​​Now perform a hypothesis test to examine the claim that the proportion of Black people killed by police in the US is different from 12.6% (the 2014 demographic percentage for Black Americans in the US population).

      1. Clearly state the null and alternative hypotheses to test, both as sentences and using symbols.

      2. Are the conditions (independent data and large enough sample size) met?

      3. ​​​​​​​Use technology to calculate the test statistic and the P-value.

      4. Make a sketch showing the distribution and the P-value.

      5. Using significance level 0.05, do you reject the null hypothesis or not?

      6. Communicate the conclusion of your hypothesis test in context.

Answer 1

Ho :   p =    0.164                  
H1 :   p ╪   0.164       (Two tail test)          
                          

Condition are met as npq >10

Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   183                  
Sample Size,   n =    1093                  
                          
Sample Proportion ,    p̂ = x/n =    0.1674                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0112                  
Z Test Statistic = ( p̂-p)/SE = (   0.1674   -   0.164   ) /   0.0112   =   0.3062
                          

                          
p-Value   =   0.7595 [excel formula =2*NORMSDIST(z)]             
Decision:   p value>α ,do not reject null hypothesis

                      
There is not enough evidence that proportion is different than 0.164

2)

Ho :   p =    0.126                  
H1 :   p ╪   0.126       (Two tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   266                  
Sample Size,   n =    1093                  
                          
Sample Proportion ,    p̂ = x/n =    0.2434                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0100                  
Z Test Statistic = ( p̂-p)/SE = (   0.2434   -   0.126   ) /   0.0100   =   11.6927
                          
  
                          
p-Value   =   0.00000 [excel formula =2*NORMSDIST(z)]              
Decision:   p-value<α , reject null hypothesis                       
There is enough evidence that proportion of black people are different than 0.124

  

THANKS

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