Does cell phone use while driving impair reaction times? One study used 32 stude

Question

Does cell phone use while driving impair reaction times? One study used 32 students at a US university to explore this question. Using a machine that simulated driving situations, at irregular periods a target would flash red or green. The participant was instructed to press a brake button as soon as they saw a red light flash. Students went through the exercise two different times, once while listening to the radio and another time while talking a political issue on a cell phone. For each of the trials, their mean response time was using the cell phone and not average difference between their reaction time while using a cell phone was 50.6 milliseconds (sd = 52.5). Based on this study, can we conclude at the 50% significance level that cell phone use leads to slower reaction times? Give the corresponding 50% confidence interval for the parameter of interest.

Explanation / Answer

Data:     

n = n1 = n2 = 32    

d-bar = 50.6    

s (of d) = 52.5    

Hypotheses:     

Ho: 1 = 2     

Ha: 1 2     

Decision Rule:    

= 0.05    

Degrees of freedom = 32 - 1 = 31

Lower Critical t- score = -2.039513438   

Upper Critical t- score = 2.039513438   

Reject Ho if |t| > 2.039513438   

Test Statistic:     

SE = s/n = 52.5/32 = 9.280776503   

t = d-bar/SE = 50.6/9.28077650307343 = 5.45213   

p- value = 5.87321E-06    

Decision (in terms of the hypotheses):    

Since 5.45213 > 2.04 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence that the mean difference is not 0

n1 = n2 = n = 32

d-bar = 50.6

s of d-bar = 52.5

% = 95

Degrees of freedom = n - 1 = 31

SE = s/n = 9.280776503

t- score = 2.039513438

Width of the confidence interval = t * SE = 18.9282684

Lower limit of the confidence interval = d-bar - width = 31.6717316

Upper limit of the confidence interval = d-bar + width = 69.5282684

The 95% confidence interval is [31.67, 69.53]

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