Experiments on learning in animals sometimes measure how long it takes a mouse t

Question

Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. Long experience indicates that the mean time is 20 seconds for one particular maze. A researcher thinks that playing loud rap music will, on average, cause mice to take longer to complete the maze.
(a) State the null and the alternative hypothesis in this case. Define (in words) the parameter of interest in this case. [8 pts]

A total of 12 mice attempted the maze while loud rap music was being played. The mean and standard deviation of the times to complete the maze are given below.

   = 22.40 seconds S = 3.58 seconds

(b) Compute the value for the test statistic (t0) in this case and use the t table to find bounds on the corresponding p-value. [7 pts]

(c) Can you reject the null hypothesis at the 5% level of significance? Explain. [7 pts]


(d) Write a conclusion in the context of the problem. [8 pts]

(e) Find a 90% confidence interval for the mean time for mice to complete the maze with the loud rap music. [8 pts]

Explanation / Answer

here null hypothesis: mean =20

alternate hypothesis: mean >20

b) std error =std deviation/(n)1/2 =1.033

hence test stat t=(X-mean)/std error =(22.4-20)/1.033=-2.3223

p value =0.0202

c) as p value is less then 0.05 level we reject null hypothesis

d) we have suffiicient evidence to conclude that playing loud rap music will, on average, cause mice to take longer to complete the maze

e) for 90% CI and 11 deree of freedom t =1.796

hence confidence interval =sample mean -/+ t*Std error =20.5440 ; 24.2560

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