Question

1. The Federal Aviation Administration wants to determine the effect of alcohol on reaction time (apparently, they really want to know how much booze a pilot can have before flying an airplane carrying hundreds of people). They conduct reaction time tests (measured in milliseconds, ms) on 10 pilots before and after consuming alcohol. Does alcohol affect reaction time? Data are seen below.

1. Conduct a hypothesis test and construct a 95% C.I. for the pre/post test difference in reaction time.

1. The Federal Aviation Administration wants to determine the effect of alcohol on reaction time (apparently, they really want to know how much booze a pilot can have before flying an airplane carrying hundreds of people). They conduct reaction time tests (measured in milliseconds, ms) on 10 pilots before and after consuming alcohol. Does alcohol affect reaction time? Data are seen below.

1. Conduct a hypothesis test and construct a 95% C.I. for the pre/post test difference in reaction time.

1. The Federal Aviation Administration wants to determine the effect of alcohol on reaction time (apparently, they really want to know how much booze a pilot can have before flying an airplane carrying hundreds of people). They conduct reaction time tests (measured in milliseconds, ms) on 10 pilots before and after consuming alcohol. Does alcohol affect reaction time? Data are seen below.

1. Conduct a hypothesis test and construct a 95% C.I. for the pre/post test difference in reaction time.

= 195.6 ms

S_d = 230.53 ms

N_p = 10

= 195.6 ms

S_d = 230.53 ms

N_p = 10

= 195.6 ms

S_d = 230.53 ms

N_p = 10

Answer 1

sample size ,    n =    10          
Degree of freedom, DF=   n - 1 =    9   and α =    0.05  
t-critical value =    t α/2,df =    2.2622   [excel function: =t.inv.2t(α/2,df) ]      
                  
std dev of difference , Sd =        230.5300          
                  
std error , SE = Sd / √n =    230.5300   / √   10   =   72.9000
margin of error, E = t*SE =    2.2622   *   72.9000   =   164.9112
                  
mean of difference ,    D̅ =   195.600          
confidence interval is                   
Interval Lower Limit= D̅ - E =   195.600   -   164.9112   =   30.6888
Interval Upper Limit= D̅ + E =   195.600   +   164.9112   =   360.5112
                  
so, confidence interval is (   31   < µd <   361   )  

---------------------------

Ho :   µd=   0                  
Ha :   µd ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
sample size ,    n =    10                  
                          
mean of sample 1,    x̅1=   0.000                  
                          
mean of sample 2,    x̅2=   0.000                  
                          
mean of difference ,    D̅ =    195.6000                  
                          
std dev of difference , Sd =        230.5300                  
                          
std error , SE = Sd / √n =    230.5300   / √   10   =   72.9000      
                          
t-statistic = (D̅ - µd)/SE = (   195.6   -   0   ) /    72.9000   =   2.683
                          
Degree of freedom, DF=   n - 1 =    9                  
  
                          
p-value =        0.0251   [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis                      

Hence alchohol effect reaction time.

Please let me know in case of any doubt.

Thanks in advance!

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