a) This is a good idea in designing the experiment because it controls for any “learning” that may occur in using the simulators.
b) 95% confidence interval :
First we need to find the differences (d) = impaired - Normal
Then we have to find the mean of differences and standard deviation of differences Sd using the excel function =AVERAGE() and STDEV.S() respectively.
= 0.9689 and Sd = 0.3643
Lower bound = - E
Upper bound = + E
E = ; t is critical value follows t distribution with degrees of freedom (df) = n-1
We are given confidence level = 0.95
We can find critical value using excel function =TINV( α , d.f )
α = 1 - confidence level = 1 - 0.95 = 0.05
degrees of freedom (d.f) = n - 1 = 9-1 = 8
t =TINV(0.05,8)
t = 2.306
Therefore,
E =
E = 0.28
Lower bound = - E = 0.9689 - 0.28 = 0.689
Upper bound = + E = 0.9689 + 0.28 = 1.249
95% Confidence interval is ( 0.689,1.249 )
Conclusion : As confidence interval does not contain 0 ;
There is sufficient evidence to conclude that there is difference in braking time with impaired vision and normal vision .
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