Question

Researchers collected data on the numbers of hospital admissions resulting from motor vehicle​ crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a​ Friday, the numbers of hospital admissions from motor vehicle crashes are not affected. Friday the​ 6th: 9 6 12 12 4 4 Friday the​ 13th: 13 12 15 11 6 10

Answer 1

paired t test

Ho :   µd=   0
Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
9	13	-4	0.4444
6	12	-6	7.1111
12	15	-3	0.1111
12	11	1	18.7778
4	6	-2	1.7778
4	10	-6	7.1111

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	47	67	-20	35.333

mean of difference ,    D̅ =ΣDi / n =   -3.3333
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.6583

std error , SE = Sd / √n =    2.6583   / √   6   =   1.0853      
                          
t-statistic = (D̅ - µd)/SE = (   -3.333 -   0   ) /    1.0853   =   -3.071

                          
Degree of freedom, DF=   n - 1 =    5                  
p-value =        0.0277 [excel function: =t.dist.2t(t-stat,df) ]               
Conclusion:     p-value <α , Reject null hypothesis      

there is enough evidence to reject the claim that when the 13th day of a month falls on a​ Friday, the numbers of hospital admissions from motor vehicle crashes are not affected