In a study to assess the effects of malaria infection on mosquito hosts, mosquit
ID: 3172857 • Letter: I
Question
In a study to assess the effects of malaria infection on mosquito hosts, mosquitoes were fed on either infective or noninfective rhesus monkeys. Subsequently, the distance x they flew during a 24-hour period was measured using a flight mill. The mosquitoes were divided into four categories of eight mosquitoes each: infective rhesus and sporozites present (IRS), infective rhesus and oocysts present (IRD), infective rhesus and no infection developed (IRN), and noninfective (C). The summary data values are: Identify I, J and n. Use the summary data provided to compute the mean square for treatments (MSTr) and the mean square for error (MSE). State the ANOVA null hypothesis and alternative in words in the context of this problem. Compute the value of the ANOVA F-test statistic. State the distribution of the test statistic. Find the critical value of this distribution (using alpha = 0.05) and compare it to the test statistic value. Formulate your conclusion.Explanation / Answer
a. The number of groups or categories is denoted by J, which is 4 and I denotes number of mosquitoes in each group, that is 8. The total number of observations is denoted by n=8*4=32.
Compute the grand mean, xbar..= (4.39+4.52+5.49+6.36)/4=20.76/4=5.19
SSTR=n1(x1bar-xbar..)^2+n2(x2bar-xbar..)^2+n3(x3bar-xbar..)+n4(x4bar-xbar..)
=8(4.39-5.19)^2+8(4.52-5.19)^2+8(5.49-5.19)^2+8(6.36-5.19)^2
=20.3824
MSTR=SSTR/J-1
=20.3824/(4-1)
=6.79 (ans)
SST=Sigma x^2ij-Nxbar^2..
=911.91-32*5.19^2
=49.9548
SSE=SST-SSTr
=49.9548-20.3824
=29.5708
MSE=SSE/n-J
=29.5708/(32-4)
=1.0561 (ans)
b. H0: mu1=mu2=mu3=mu4 (there is no difference in mean distance x flew by four different types of mosquitoes)
H1:atleats one mean is different
c. F=MSTR/MSE
=6.79/1.0561
=6.43
F(Critical) at alpha=0.05, and df(3, 28) is: 2.94
Per rule, reject H0, if observed test statistic falls in critical region [observed(F)>=Critical(F)]. Here, F test statistic falls in critical region, therefore, reject H0 and conclude that atleast one mean distance flew by one type of mosquito is significantly different from another.
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