Question

we are trying to do a project and we are not sure whether to accept or reject the hypothesis. We have the chi square (we think it is correct) We aren't sure how to do the last steps.

H0:There is no difference in police killing counts based on race That is, race does not make a difference in the number of killings by race, and any differences can be attributed to the natural variations of randomness.

H1: There is a difference in police killings counts based on race. that is, race does make a difference in the number of police killings by race

What conclusions, if any, do you believe you can draw because of your study? If the results were not what you expected, what factors might explain your results? What did you learn from your project about the population(s) you studied? What did you learn about the research variables. What did you learn about the specific statistical test you conducted?

differnces^2	5.0176	17.64	6.9696	0	0	15.3664	3.24	0	0.9216	0
differnces ^2/expected	2.85090909	6.3	19.36	0	0	4.98909091	2.7	0	23.04	0
chi square	59.24
		2015				2016
VA	b	w	h	a	o	b	w	h	a	o
	10	7	1	0	0	8	8	1	0	0
	5.1429	3	0.0571	0	0	3.4286	3.4286	0.0571	0	0
differences	4.8571	4	0.9429	0	0	4.5714	4.5714	0.9429	0	0
differnces^2	23.5914204	16	0.88906041	0	0	20.897698	20.897698	0.88906041	0	0
differnces ^2/expected	4.58718241	5.33333333	15.5702349	0	0	6.09511111	6.09511111	15.5702349	0	0
chi square	53.2512077

We have five race categories, so we need to find the chi-suqare value with 4 degrees of freedon.

We have two conditions for chi square value test that need to be satisfied:

1: Independence: we have no reason to believe that any killing that any case of a police officer killing is not independent of another case of police killing.

Answer 1

The above test is not conducted properly. The sum of observed values must be equal to the sum of expected values for both the years together but you can see they are not equal. If the given observed values(number of police killings) given are correct, then the Chi-square test statistic of the test is to be calculated as follows:

At 5% significance level, with degrees of freedom =4, the critical value of Chi-square is 9.488

Since the test statistic: 44 > critical value:9.488, we reject the null hypothesis at 0.05 significance level and conclude that there is a sufficient evidence to claim there is a difference in police killings counts based on race, that is, race does make a difference in the number of police killings by race. (That is, the differences cannot be attributed to the natural variations of randomness​​​​​​).

So, the independent nominal variable, race (with 5 categories) significantly influenced the dependent variable, police killings during the period of 2015 and 2016.

​The specific statistical test, i.e., Chi-square test for observed and expected frequencies conducted above is useful to identify if there is a significant difference between observed and expected frequencies (here, number of police killings) at the desired significance level (here, 0.05) and here, the test provided evidence for the significant difference.