An experiment was conducted to explore the effects of extended periods of sensor
ID: 3156049 • Letter: A
Question
An experiment was conducted to explore the effects of extended periods of sensory deprivation on alpha-wave frequencies which are an indicator of brain activity. (Alpha-wave frequencies can be determined via an EEG (electro-encephalogram).) Higher alpha-wave frequencies are generally associated with lower levels of stress and anxiety. Twenty volunteers, all of whom were inmates in a Canadian prison, were randomly divided into two groups of ten inmates. The members of one group were placed in solitary confinement and were allowed no contact with other inmates (isolated). The members of the other group were allowed to remaIn their usual cells and were allowed normal contact with other inmates (not isolated). After seven days under these conditions, alpha wave frequencies were measured for each inmate. The data values (alpha wave frequencies, in Hertz (Hz)) are given below, (source: P. Gendreau et al. (1972), Journal of Abnormal Psychology, 79, 54-59, as described in De Veaux and Velleman (2004)) a) Clearly define two relevant population means, mu1 and mu2, with the subscript 1 indicating "isolated" and the subscript 2 indicating "not isolated". These hypothetical population means should be defined to correspond to the population of available units (individuals). b) State what you believe to be an appropriate research hypothesis relating mu1 to mu2. Provide a clear and complete statement of this hypothesis in wrds in the context of this problem and explain why your hypothesis is appropriate. I have examined the data and found that it is reasonable to model the 10 alpha wave frequencies corresponding to the isolated inmates and the 10 alpha wave frequencies corresponding to the not isolated inmates as independent random samples from normal distributions. Thus you may assume this without chocking. c) Perform a hypothesis test for your research hypothesis. Be sure to give the P value and provide a complete summary in the context of this problem. d) Provide 95% confidence interval estimate for mu1 - mu2 and use it in a brief discussion of this example.Explanation / Answer
c) H0:mu1-mu2=0 (there is no difference in mean alpha-wave frequencies of isolated and non-isolated inmates)
H1:mu1-mu2 not equal to 0 (there is significant difference in mean alpha-wave frequencies of isolated and non-isolated inmates)
From information given, x1bar=9.78, s1=0.598, x2bar=10.580, s2=0.459, where x1bar, x2bar, s1 and s2 represent mean alphawavelengths for isolated and not-isoalated inmates, and standard deviations of isolated and non-isolated inmates.
Perform 2-sample t test to test the claim.
For independent random samples,
SE(x1bar-x2bar)=sqrt [s1^2/n1+s2^2/n2]
=sqrt[0.598^2/10+0.459^2/10]
=0.238
t=[(x1bar-x2bar)-0]/SE(x1bar-x2bar)
=(9.78-10.58)/0.238
=-3.36
The p value at df=16 is 0.004.
The p value is less than alpha=0.05. Reject null hypothesis to conclude that there is significant difference in mean alpha-wave frequencies of isolated and non-isolated inmates.
d) 95% c.i=(x1bar-x2bar)+-tcritical SE(x1bar-x2bar)
=(9.780-10.580)+-2.120*0.238
=-1.305 to -0.295
one can be 95% confident that the interval captures the mean amount of alpha-wave frequency of isolated and non-isolated inmates.
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