Two Related Samples t-test Prof Awesome is a behavioral neuroscientist intereste

Question

Two Related Samples t-test Prof Awesome is a behavioral neuroscientist interested in studying the function of the amygdala -a part of the brain that appears to control responses to fearful stimuli. He hypothesizes that ablation (i.e., destruction) ofthe amygdala should show some effect on the ability of mice to respond to a predator. To test his hypothesis Prof. Awesome recorded the amount of time 10 mice spent hiding behind a wooden block once a rubber snake was introduced into their cage, both before and after surgical ablation ofthe amygdala. The time the mice spent hiding behind the wooden block was used to measure the strength of their fear response more time spent hiding representing a stronger fear response. The data he collected is tabled below. Time (min) Spent Hiding Time (min) Spent Hiding Mouse Before Ablation of Amygdala After Ablation of Amygdala 10 5 Mean 2.8 2.38 SD 1. What is your null and altemative hypothesis (in words AND symbols? (Remember: You need to state these hypotheses in tems of population means!) (5pt) 2. Calculate the t-test statistic and all the required intemediate steps (20 pts)

Explanation / Answer

(a) Ho. There is no mean difference between the response times and Ha: There is a significant difference between the response times

Ho: d = 0 and Ha: d 0

(b)

Data:     

n = n1 = n2 = 10    

d-bar = -3.9    

s (of d) = 2.330951165    

Hypotheses:     

Ho: 1 = 2     

Ha: 1 2     

Test Statistic:   

SE = s/n = 2.33095116493961/10 = 0.73711148   

t = d-bar/SE = -3.9/0.737111479583199 = -5.29092289

Decision Rule:    

= 0.05    

Degrees of freedom = 10 - 1 = 9

Lower Critical t- score = -2.262157158   

Upper Critical t- score = 2.262157158   

Reject Ho if |t| > 2.262157158

Decision (in terms of the hypotheses):

Since 5.29092289 > 2.262 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence of a difference in the mean response times

Before After d = After - Before 2 1 -1 4 2 -2 4 1 -3 7 3 -4 7 2 -5 8 2 -6 9 3 -6 9 9 0 10 5 -5 10 3 -7 d-bar = -3.9 s = 2.330951165

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