q4

Analysis 4

4a: My ID number is [20949813] and I will be comparing subject.race in San Francisco

4b:

Sample Statistic	Non-White	White
Size	286	208
Mean	3.523	3.667
Median	3.497	3.664
Standard Deviation	0.335	0.345

4c: To test $H_0:{\mu }_0={\mu }_1$, we use an unpaired test because for this study, it is reasonable to assume the 2 groups (white and non-white) are independent of each other. The observed

value of the test statistic is calculated by

$d=\frac{|\overline{y_1}-\overline{y_2}-0|}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

From the above:

• $y_1$: This is the mean for non-white group = value above in table
• $y_2$: This is the mean for white group = value above in table
• $s_p$: This is the pooled standard deviation = 0.339
• $n_1$: This is sample size of non-white group = value above in table
• $n_2$: This is the sample size of white group = value above in table

The value of the test statistic for my sample is -4.678. To calculate the p-value we perform the following computation:

$2(1-P(T\le -4.678))$

Where T is a T-distribution with 286 + 208 - 1 = 493 degrees of freedom. The resulting p-value is 0.00000376.

4d: The results in Analysis 4c rely on the following assumptions:

• The 2 sample groups (white and non-white) are independent of each other
• The above also assumes there is equal variance between the 2 sample groups. In particular, we have assumed that they have the same variance subject.age

4e: Based on the results of Analysis 4c, I conclude:

• given the very small p-value, where it is < 0.1, there is compelling evidence arguing against the null hypothesis. Thus, we can say that there is strong evidence that race-based traffic stops exists.