Researchers collected data on the numbers of hospital admiss

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: 10 7 12 12 4 6

Friday the 13th: 14 13 14 11 6 14

Find the value test statistic.

Solution

As the same hispitals are involved, we do a paired t test.

Let ud = u2 - u1.              

Where

u2 = mean of 13th
u1 = mean of 6th
Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    1.894122914          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    0.773272442          
              
Calculating the mean of the differences (third column):              
              
XD =    3.5          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    4.526218461   [ANSWER]