A researcher is interested in determining the effects of sleep deprivation on th

Question

A researcher is interested in determining the effects of sleep deprivation on the length of time it takes rats to correctly travel a maze to its end point. researcher wants to know whether the amount of The sleep deprivation makes a difference in the speed with which the rats correctly travel the maze. The researcher begins with twenty rats and randomly assigns them to one of two groups such that there are ten rats in each group. One group of 10 rats is sleep deprived for 24 hours prior to performing in the maze, and the second group of 10 rats is sleep deprived for 36 hours before performing in the maze. The researcher records the length of time (in seconds it takes for each rat to correctly run the maze. The following data were recorded for each rat in each group: Group 2 (36 hour deprivation) Group 1 (24 hour deprivation) 14 16 16 With a 05, summarize the results of the hypothesis testing procedure by putting your results in journal form. Ignore the minus sign if your calculated z or t is negative.

Explanation / Answer

Hypotheses:

H0: mu1-mu2=0 (there is no difference in time taken to correctly run the maze for group 1 and group 2 rats)

H1:mu1-mu2=/=0 (there is difference in time taken to correctly run the maze for group1 and group2 rats)

Assume Independent group assumption, Independence assumption, Randomization condition and Nearly normal conditions are reasonably met.

Therefore, for two independent groups, perform 2-sample t test.

Computational formual for xbar=sigma x/n, and s=sqrt[1/n-1 sigma (x-xbar)^2].

Using the formula the sample standard deviation for group1 and 2 are 2.331 and 2.547, both sample sizes are equal, therefore, obtain the ratio of s1 to s2. s1/s2=0.9<2. Therefore, use pooled variance.

sp=sqrt[{(n1-1)s1^2+(n2-1)s2^2}/(n1+n2-2)]

=sqrt[{9*2.331^2+9*2.547^2}/(10+10-2)]

=2.4415

t=(x1bar-x2bar)/sp sqrt(1/n1+1/n2)

=(10.10-13.40)/2.4415 sqrt(1/10+1/10)

=-3.02

p value at 18 degrees of freedom [df=n1+n2-2] is 0.007.

Therefore, t(18)=3.02, p<0.05

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